Master File
Joanna Duran, Nikhil Gupta, Max Moro
2019-04-01 22:34:43
User Inputs
output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = params$norm.pred
eda = params$eda
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 9
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ norm.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.var
# output.var.tr = if (log.pred == TRUE) paste0(output.var,'.cuberoot') else output.var.tr = output.var
# output.var.tr = if (norm.pred == TRUE) paste0(output.var,'.bestnorm') else output.var.tr = output.varLoading Data
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')Data validation
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))## Original cases: 10000message('Non-Complete cases: ',nrow(data.notComplete))## Non-Complete cases: 3020message('Complete cases: ',nrow(data))## Complete cases: 6980summary(dplyr::select_at(data,c('JobName',output.var)))## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974Output Variable
The Output Variable y3 shows right skewness, so will proceed with a log transformation
Histogram
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() 
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value))) QQPlot
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Trasformation of Output Variable from y3 to y3.log
if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
# if(log.pred==TRUE) data[[output.var.tr]] = (data[[output.var]])^(1/3) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Best Normalizator y3
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
if (norm.pred == TRUE){
t=bestNormalize::bestNormalize(data[[output.var]])
t
qqnorm(data[[output.var]])
qqnorm(predict(t))
data[[output.var.tr]] = predict(t)
}orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
Predictors
Feature Engineering
data$x2byx1 = data$x2/data$x1
data$x6byx5 = data$x6/data$x5
data$x9byx7 = data$x9/data$x7
data$x10byx8 = data$x10/data$x8
data$x14byx12 = data$x14/data$x12
data$x15byx13 = data$x15/data$x13
data$x17byx16 = data$x17/data$x16
data$x19byx18 = data$x19/data$x18
data$x21byx20 = data$x21/data$x20
data$x23byx22 = data$x23/data$x22
data$x1log = log(data$x1)
data$x2log = log(data$x2)
data$x5log = log(data$x5)
data$x6log = log(data$x6)
data$x7log = log(data$x7)
data$x9log = log(data$x9)
data$x8log = log(data$x8)
data$x10log = log(data$x10)
data$x12log = log(data$x12)
data$x14log = log(data$x14)
data$x13log = log(data$x13)
data$x15log = log(data$x15)
data$x16log = log(data$x16)
data$x17log = log(data$x17)
data$x18log = log(data$x18)
data$x19log = log(data$x19)
data$x20log = log(data$x20)
data$x21log = log(data$x21)
data$x22log = log(data$x22)
data$x23log = log(data$x23)data$x11log = log(data$x11)data$x1sqinv = 1/(data$x1)^2
data$x5sqinv = 1/(data$x5)^2
data$x7sqinv = 1/(data$x7)^2
data$x8sqinv = 1/(data$x8)^2
data$x12sqinv = 1/(data$x12)^2
data$x13sqinv = 1/(data$x13)^2
data$x16sqinv = 1/(data$x16)^2
data$x18sqinv = 1/(data$x18)^2
data$x20sqinv = 1/(data$x20)^2
data$x22sqinv = 1/(data$x22)^2 print("Predictors before feature engineering")## [1] "Predictors before feature engineering"print (predictors)## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10" "x11"
## [12] "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20" "x21" "x22"
## [23] "x23" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6" "stat7" "stat8" "stat9" "stat10"
## [34] "stat11" "stat12" "stat13" "stat14" "stat15" "stat16" "stat17" "stat18" "stat19" "stat20" "stat21"
## [45] "stat22" "stat23" "stat24" "stat25" "stat26" "stat27" "stat28" "stat29" "stat30" "stat31" "stat32"
## [56] "stat33" "stat34" "stat35" "stat36" "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43"
## [67] "stat44" "stat45" "stat46" "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54"
## [78] "stat55" "stat56" "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65"
## [89] "stat66" "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [100] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86" "stat87"
## [111] "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96" "stat97" "stat98"
## [122] "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106" "stat107" "stat108" "stat109"
## [133] "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116" "stat117" "stat118" "stat119" "stat120"
## [144] "stat121" "stat122" "stat123" "stat124" "stat125" "stat126" "stat127" "stat128" "stat129" "stat130" "stat131"
## [155] "stat132" "stat133" "stat134" "stat135" "stat136" "stat137" "stat138" "stat139" "stat140" "stat141" "stat142"
## [166] "stat143" "stat144" "stat145" "stat146" "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153"
## [177] "stat154" "stat155" "stat156" "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164"
## [188] "stat165" "stat166" "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175"
## [199] "stat176" "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [210] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196" "stat197"
## [221] "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206" "stat207" "stat208"
## [232] "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216" "stat217"controlled.vars = colnames(data)[grep("^x",colnames(data))]
stat.vars = colnames(data)[grep("^stat",colnames(data))]
predictors = c(controlled.vars,stat.vars)
print("Predictors after feature engineering")## [1] "Predictors after feature engineering"print (predictors)## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10"
## [11] "x11" "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20"
## [21] "x21" "x22" "x23" "x2byx1" "x6byx5" "x9byx7" "x10byx8" "x14byx12" "x15byx13" "x17byx16"
## [31] "x19byx18" "x21byx20" "x23byx22" "x1log" "x2log" "x5log" "x6log" "x7log" "x9log" "x8log"
## [41] "x10log" "x12log" "x14log" "x13log" "x15log" "x16log" "x17log" "x18log" "x19log" "x20log"
## [51] "x21log" "x22log" "x23log" "x11log" "x1sqinv" "x5sqinv" "x7sqinv" "x8sqinv" "x12sqinv" "x13sqinv"
## [61] "x16sqinv" "x18sqinv" "x20sqinv" "x22sqinv" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6"
## [71] "stat7" "stat8" "stat9" "stat10" "stat11" "stat12" "stat13" "stat14" "stat15" "stat16"
## [81] "stat17" "stat18" "stat19" "stat20" "stat21" "stat22" "stat23" "stat24" "stat25" "stat26"
## [91] "stat27" "stat28" "stat29" "stat30" "stat31" "stat32" "stat33" "stat34" "stat35" "stat36"
## [101] "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43" "stat44" "stat45" "stat46"
## [111] "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54" "stat55" "stat56"
## [121] "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65" "stat66"
## [131] "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [141] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86"
## [151] "stat87" "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96"
## [161] "stat97" "stat98" "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106"
## [171] "stat107" "stat108" "stat109" "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116"
## [181] "stat117" "stat118" "stat119" "stat120" "stat121" "stat122" "stat123" "stat124" "stat125" "stat126"
## [191] "stat127" "stat128" "stat129" "stat130" "stat131" "stat132" "stat133" "stat134" "stat135" "stat136"
## [201] "stat137" "stat138" "stat139" "stat140" "stat141" "stat142" "stat143" "stat144" "stat145" "stat146"
## [211] "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153" "stat154" "stat155" "stat156"
## [221] "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164" "stat165" "stat166"
## [231] "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175" "stat176"
## [241] "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [251] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196"
## [261] "stat197" "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206"
## [271] "stat207" "stat208" "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216"
## [281] "stat217"All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Interesting Predictors
Histograms
if (eda == TRUE){
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
lapply(select_at(data,cols),summary)
}Scatter plot vs. output variable **y3.log
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)
}All Predictors
Histograms
All indicators have a strong indication of Fat-Tails
if (eda == TRUE){
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
}Correlations
With Output Variable
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
# https://stackoverflow.com/questions/27034655/how-to-use-dplyrarrangedesc-when-using-a-string-as-column-name
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
#rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-!!sym(output.var.tr))
}if (eda == TRUE){
message("Top Positive")
#kable(head(arrange(t,desc(y3.log)),20))
kable(head(arrange(t,desc(!!sym(output.var.tr))),20))
}if (eda == TRUE){
message("Top Negative")
#kable(head(arrange(t,y3.log),20))
kable(head(arrange(t,!!sym(output.var.tr)),20))
}Between All Variables
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")
kable(t[1:10,1:10])
}Scatter Plots with Output Variable
Scatter plots with all predictors and the output variable (y3.log)
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
}Multicollinearity - VIF
No Multicollinearity among predictors
Showing Top predictor by VIF Value
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,75)
}Feature Eng
- Square Root transformation for x18
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')Comparing Pre and Post Transformation Density Plots
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
#dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('JobName')])
data=data.tr
label.names=output.var.trModeling
PCA
# 0 for no interaction,
# 1 for Full 2 way interaction and
# 2 for Selective 2 way interaction
# 3 for Selective 3 way interaction
InteractionMode = 2
pca.vars = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
if(InteractionMode == 1){
pca.formula =as.formula(paste0('~(',paste0(pca.vars, collapse ='+'),')^2'))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
#saveRDS(pca.model,'pca.model.rds')
}
if (InteractionMode == 0){
pca.model = prcomp(x=data[,pca.vars],center=T,scale.=T,retx = T)
}
if (InteractionMode >= 2 & InteractionMode <= 3){
controlled.vars = pca.vars[grep("^x",pca.vars)]
stat.vars = pca.vars[grep("^stat",pca.vars)]
if (InteractionMode >= 2){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^2')
}
if (InteractionMode >= 3){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^3')
}
no.interact.form = paste0(stat.vars, collapse ='+')
pca.formula = as.formula(paste(interaction.form, no.interact.form, sep = "+"))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
}
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymoretargetCumVar = .9
pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")## 164 PCAs justify 90.0% of the total Variance. (90.0%)plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained", type='b')
plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')
screeplot(pca.model,npcs = pca.model$pcaSelCount)
screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')
#summary(pca.model)
#pca.model$rotation
#creating dataset
data.pca = dplyr::select(data,!!label.names) %>%
dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
,!!colnames(pca.model$rotation)[pca.model$pcaSel])
)Train Test Split
data.pca = data.pca[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)
data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = 0,size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
df = data.frame(x=predict(model,train),y=r.standard)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
else if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
else if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
else if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE:", test.rmse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
x = 10^test[,label.names]
y = 10^pred[,1]
# x = (test[,label.names])^3
# y = (pred[,1])^3
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
test.mse = mean((x-y)^2)
print (paste(method, subopt, "Test MSE (Org Scale):", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE (Org Scale):", test.rmse, sep=" "))
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3.log ~ PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 + PC9 +
## PC10 + PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 + PC18 +
## PC19 + PC20 + PC21 + PC22 + PC23 + PC24 + PC25 + PC26 + PC27 +
## PC28 + PC29 + PC30 + PC31 + PC32 + PC33 + PC34 + PC35 + PC36 +
## PC37 + PC38 + PC39 + PC40 + PC41 + PC42 + PC43 + PC44 + PC45 +
## PC46 + PC47 + PC48 + PC49 + PC50 + PC51 + PC52 + PC53 + PC54 +
## PC55 + PC56 + PC57 + PC58 + PC59 + PC60 + PC61 + PC62 + PC63 +
## PC64 + PC65 + PC66 + PC67 + PC68 + PC69 + PC70 + PC71 + PC72 +
## PC73 + PC74 + PC75 + PC76 + PC77 + PC78 + PC79 + PC80 + PC81 +
## PC82 + PC83 + PC84 + PC85 + PC86 + PC87 + PC88 + PC89 + PC90 +
## PC91 + PC92 + PC93 + PC94 + PC95 + PC96 + PC97 + PC98 + PC99 +
## PC100 + PC101 + PC102 + PC103 + PC104 + PC105 + PC106 + PC107 +
## PC108 + PC109 + PC110 + PC111 + PC112 + PC113 + PC114 + PC115 +
## PC116 + PC117 + PC118 + PC119 + PC120 + PC121 + PC122 + PC123 +
## PC124 + PC125 + PC126 + PC127 + PC128 + PC129 + PC130 + PC131 +
## PC132 + PC133 + PC134 + PC135 + PC136 + PC137 + PC138 + PC139 +
## PC140 + PC141 + PC142 + PC143 + PC144 + PC145 + PC146 + PC147 +
## PC148 + PC149 + PC150 + PC151 + PC152 + PC153 + PC154 + PC155 +
## PC156 + PC157 + PC158 + PC159 + PC160 + PC161 + PC162 + PC163 +
## PC164print(grand.mean.formula)## y3.log ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Scatter plots with all PCAs and the output variable (y3.log)
d = gather(dplyr::select_at(data.pca,c(feature.names,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#chart.Correlation(select(data,-JobName), pch=21)
# https://stackoverflow.com/questions/27034655/how-to-use-dplyrarrangedesc-when-using-a-string-as-column-name
t=as.data.frame(round(cor(dplyr::select(data.pca,-one_of(output.var.tr))
,select_at(data,output.var.tr)),4)) %>%
rownames_to_column(var='variable') %>% arrange(-!!sym(output.var.tr))message("Top Positive")## Top Positivekable(head(arrange(t,desc(!!sym(output.var.tr))),20))| variable | y3.log |
|---|---|
| PC121 | 0.0381 |
| PC87 | 0.0319 |
| PC137 | 0.0309 |
| PC68 | 0.0287 |
| PC149 | 0.0266 |
| PC40 | 0.0237 |
| PC49 | 0.0228 |
| PC56 | 0.0219 |
| PC125 | 0.0218 |
| PC4 | 0.0216 |
| PC43 | 0.0196 |
| PC67 | 0.0194 |
| PC85 | 0.0194 |
| PC42 | 0.0189 |
| PC156 | 0.0171 |
| PC96 | 0.0165 |
| PC83 | 0.0161 |
| PC90 | 0.0160 |
| PC133 | 0.0156 |
| PC153 | 0.0142 |
message("Top Negative")## Top Negativekable(head(arrange(t,!!sym(output.var.tr)),20)) | variable | y3.log |
|---|---|
| PC128 | -0.0287 |
| PC76 | -0.0251 |
| PC12 | -0.0219 |
| PC94 | -0.0215 |
| PC54 | -0.0213 |
| PC160 | -0.0210 |
| PC164 | -0.0204 |
| PC70 | -0.0200 |
| PC13 | -0.0197 |
| PC63 | -0.0196 |
| PC115 | -0.0196 |
| PC8 | -0.0190 |
| PC14 | -0.0184 |
| PC124 | -0.0181 |
| PC139 | -0.0179 |
| PC143 | -0.0171 |
| PC81 | -0.0161 |
| PC98 | -0.0159 |
| PC9 | -0.0156 |
| PC145 | -0.0153 |
Full Model
Train
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.085666 -0.022260 -0.005973 0.017026 0.187630
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.097e+00 4.248e-04 4936.182 < 2e-16 ***
## PC1 -4.990e-04 3.722e-05 -13.407 < 2e-16 ***
## PC2 -9.427e-04 3.756e-05 -25.099 < 2e-16 ***
## PC3 -4.374e-04 3.819e-05 -11.451 < 2e-16 ***
## PC4 -3.242e-04 3.850e-05 -8.420 < 2e-16 ***
## PC5 1.771e-04 3.927e-05 4.509 6.64e-06 ***
## PC6 -9.229e-05 3.957e-05 -2.332 0.019727 *
## PC7 -2.087e-04 4.056e-05 -5.146 2.75e-07 ***
## PC8 -4.702e-05 4.134e-05 -1.137 0.255483
## PC9 -3.963e-05 4.206e-05 -0.942 0.346149
## PC10 -1.822e-05 4.303e-05 -0.423 0.671956
## PC11 -5.806e-04 4.599e-05 -12.625 < 2e-16 ***
## PC12 -4.674e-04 4.845e-05 -9.647 < 2e-16 ***
## PC13 2.936e-04 4.939e-05 5.945 2.94e-09 ***
## PC14 2.353e-04 5.110e-05 4.605 4.23e-06 ***
## PC15 -3.852e-05 5.196e-05 -0.741 0.458548
## PC16 3.066e-04 5.253e-05 5.837 5.61e-09 ***
## PC17 -1.704e-04 5.536e-05 -3.078 0.002096 **
## PC18 -3.526e-04 5.747e-05 -6.135 9.12e-10 ***
## PC19 7.502e-05 5.843e-05 1.284 0.199217
## PC20 4.102e-04 6.384e-05 6.425 1.43e-10 ***
## PC21 9.972e-05 6.641e-05 1.502 0.133225
## PC22 1.955e-05 1.043e-04 0.187 0.851322
## PC23 2.280e-04 1.302e-04 1.751 0.079990 .
## PC24 -9.013e-04 1.502e-04 -5.999 2.11e-09 ***
## PC25 1.823e-04 1.689e-04 1.079 0.280644
## PC26 4.830e-04 1.718e-04 2.811 0.004958 **
## PC27 2.388e-04 1.757e-04 1.359 0.174232
## PC28 5.524e-05 1.764e-04 0.313 0.754150
## PC29 5.622e-04 1.938e-04 2.900 0.003744 **
## PC30 5.938e-05 1.977e-04 0.300 0.763936
## PC31 -1.741e-04 2.109e-04 -0.826 0.408981
## PC32 -7.593e-04 2.149e-04 -3.533 0.000414 ***
## PC33 4.014e-04 2.188e-04 1.834 0.066696 .
## PC34 1.089e-03 2.313e-04 4.709 2.55e-06 ***
## PC35 5.475e-05 2.500e-04 0.219 0.826681
## PC36 -5.923e-06 2.521e-04 -0.023 0.981259
## PC37 -5.339e-04 2.588e-04 -2.063 0.039171 *
## PC38 2.825e-04 2.699e-04 1.047 0.295289
## PC39 -2.365e-04 2.775e-04 -0.852 0.394132
## PC40 -2.964e-04 2.782e-04 -1.065 0.286786
## PC41 -2.661e-04 2.854e-04 -0.932 0.351271
## PC42 -3.905e-05 2.861e-04 -0.136 0.891442
## PC43 -7.003e-05 2.874e-04 -0.244 0.807533
## PC44 6.413e-04 2.910e-04 2.204 0.027589 *
## PC45 -1.101e-04 2.967e-04 -0.371 0.710514
## PC46 1.938e-04 2.962e-04 0.654 0.513086
## PC47 -5.010e-04 2.955e-04 -1.695 0.090042 .
## PC48 3.276e-04 2.952e-04 1.110 0.267183
## PC49 1.888e-04 3.021e-04 0.625 0.532092
## PC50 -2.760e-04 3.020e-04 -0.914 0.360817
## PC51 2.901e-04 3.121e-04 0.930 0.352584
## PC52 1.969e-04 3.076e-04 0.640 0.522058
## PC53 1.714e-04 3.071e-04 0.558 0.576736
## PC54 -3.426e-04 3.121e-04 -1.098 0.272334
## PC55 -2.023e-04 3.133e-04 -0.646 0.518469
## PC56 -7.202e-05 3.170e-04 -0.227 0.820282
## PC57 -1.101e-04 3.161e-04 -0.348 0.727543
## PC58 4.911e-05 3.204e-04 0.153 0.878193
## PC59 9.403e-04 3.191e-04 2.946 0.003231 **
## PC60 -2.079e-05 3.239e-04 -0.064 0.948814
## PC61 -2.193e-05 3.211e-04 -0.068 0.945538
## PC62 -4.283e-04 3.208e-04 -1.335 0.181838
## PC63 -6.550e-04 3.232e-04 -2.026 0.042777 *
## PC64 -8.981e-04 3.265e-04 -2.750 0.005970 **
## PC65 7.537e-05 3.288e-04 0.229 0.818690
## PC66 -3.764e-04 3.284e-04 -1.146 0.251736
## PC67 3.905e-04 3.299e-04 1.184 0.236651
## PC68 8.195e-04 3.299e-04 2.484 0.013032 *
## PC69 4.461e-04 3.278e-04 1.361 0.173560
## PC70 -1.399e-04 3.333e-04 -0.420 0.674811
## PC71 3.652e-04 3.346e-04 1.092 0.275058
## PC72 -3.997e-05 3.386e-04 -0.118 0.906026
## PC73 3.541e-04 3.369e-04 1.051 0.293200
## PC74 -4.960e-04 3.386e-04 -1.465 0.143032
## PC75 -8.673e-04 3.343e-04 -2.595 0.009492 **
## PC76 -3.092e-04 3.419e-04 -0.904 0.365817
## PC77 4.001e-04 3.401e-04 1.176 0.239511
## PC78 1.956e-04 3.423e-04 0.572 0.567670
## PC79 6.753e-04 3.476e-04 1.943 0.052111 .
## PC80 -3.711e-04 3.463e-04 -1.071 0.284017
## PC81 8.750e-04 3.462e-04 2.528 0.011514 *
## PC82 2.785e-04 3.489e-04 0.798 0.424863
## PC83 -7.346e-04 3.491e-04 -2.104 0.035421 *
## PC84 5.812e-04 3.540e-04 1.642 0.100637
## PC85 1.135e-03 3.530e-04 3.214 0.001315 **
## PC86 -3.229e-04 3.544e-04 -0.911 0.362383
## PC87 1.860e-03 3.536e-04 5.260 1.50e-07 ***
## PC88 -9.439e-04 3.590e-04 -2.629 0.008593 **
## PC89 -7.274e-04 3.612e-04 -2.014 0.044099 *
## PC90 -9.620e-04 3.600e-04 -2.672 0.007564 **
## PC91 8.689e-05 3.622e-04 0.240 0.810438
## PC92 -3.097e-04 3.613e-04 -0.857 0.391407
## PC93 3.876e-04 3.611e-04 1.073 0.283142
## PC94 -6.079e-04 3.643e-04 -1.669 0.095228 .
## PC95 7.706e-05 3.631e-04 0.212 0.831930
## PC96 -4.607e-04 3.664e-04 -1.257 0.208631
## PC97 -3.611e-04 3.673e-04 -0.983 0.325543
## PC98 -5.811e-04 3.659e-04 -1.588 0.112280
## PC99 -3.775e-04 3.681e-04 -1.025 0.305213
## PC100 2.517e-04 3.675e-04 0.685 0.493413
## PC101 -2.724e-05 3.664e-04 -0.074 0.940738
## PC102 -7.676e-04 3.670e-04 -2.092 0.036504 *
## PC103 5.305e-04 3.684e-04 1.440 0.149878
## PC104 -9.005e-04 3.688e-04 -2.442 0.014655 *
## PC105 9.531e-04 3.697e-04 2.578 0.009951 **
## PC106 7.088e-04 3.722e-04 1.904 0.056898 .
## PC107 1.653e-04 3.734e-04 0.443 0.658013
## PC108 2.479e-04 3.714e-04 0.667 0.504551
## PC109 1.320e-04 3.732e-04 0.354 0.723550
## PC110 -5.208e-04 3.736e-04 -1.394 0.163354
## PC111 -5.527e-04 3.726e-04 -1.483 0.138013
## PC112 -8.322e-05 3.728e-04 -0.223 0.823380
## PC113 2.552e-04 3.753e-04 0.680 0.496555
## PC114 -6.728e-04 3.736e-04 -1.801 0.071748 .
## PC115 -1.572e-03 3.795e-04 -4.142 3.49e-05 ***
## PC116 -8.203e-05 3.779e-04 -0.217 0.828161
## PC117 7.989e-06 3.808e-04 0.021 0.983264
## PC118 3.522e-04 3.785e-04 0.930 0.352180
## PC119 -8.767e-04 3.799e-04 -2.308 0.021049 *
## PC120 3.442e-04 3.786e-04 0.909 0.363321
## PC121 -4.492e-04 3.814e-04 -1.178 0.238937
## PC122 6.535e-04 3.815e-04 1.713 0.086745 .
## PC123 -6.955e-04 3.801e-04 -1.830 0.067308 .
## PC124 4.768e-04 3.810e-04 1.252 0.210742
## PC125 4.908e-04 3.852e-04 1.274 0.202656
## PC126 1.784e-05 3.814e-04 0.047 0.962708
## PC127 6.673e-04 3.824e-04 1.745 0.081032 .
## PC128 -9.621e-04 3.838e-04 -2.507 0.012212 *
## PC129 1.134e-04 3.814e-04 0.297 0.766122
## PC130 2.236e-04 3.844e-04 0.582 0.560839
## PC131 -1.130e-03 3.868e-04 -2.923 0.003486 **
## PC132 2.470e-04 3.849e-04 0.642 0.521096
## PC133 -7.617e-05 3.872e-04 -0.197 0.844055
## PC134 7.093e-04 3.869e-04 1.833 0.066849 .
## PC135 4.051e-04 3.885e-04 1.043 0.297093
## PC136 5.726e-04 3.847e-04 1.488 0.136706
## PC137 -2.995e-04 3.859e-04 -0.776 0.437735
## PC138 3.868e-04 3.883e-04 0.996 0.319193
## PC139 -9.158e-04 3.896e-04 -2.351 0.018771 *
## PC140 -4.054e-04 3.918e-04 -1.035 0.300777
## PC141 -2.103e-05 3.912e-04 -0.054 0.957134
## PC142 6.761e-05 3.890e-04 0.174 0.862017
## PC143 3.884e-04 3.921e-04 0.991 0.321968
## PC144 7.588e-04 3.907e-04 1.942 0.052190 .
## PC145 3.897e-04 3.926e-04 0.993 0.320894
## PC146 7.296e-04 3.931e-04 1.856 0.063512 .
## PC147 -2.689e-04 3.960e-04 -0.679 0.497076
## PC148 -5.673e-04 3.954e-04 -1.435 0.151395
## PC149 -5.301e-05 3.953e-04 -0.134 0.893344
## PC150 4.800e-04 3.947e-04 1.216 0.224022
## PC151 5.832e-04 3.970e-04 1.469 0.141852
## PC152 -5.386e-04 3.933e-04 -1.370 0.170840
## PC153 8.863e-04 3.952e-04 2.243 0.024958 *
## PC154 -1.036e-03 3.942e-04 -2.629 0.008582 **
## PC155 9.819e-04 3.968e-04 2.475 0.013372 *
## PC156 5.547e-04 4.002e-04 1.386 0.165752
## PC157 1.107e-04 3.987e-04 0.278 0.781183
## PC158 5.985e-06 3.976e-04 0.015 0.987990
## PC159 1.540e-03 3.952e-04 3.897 9.86e-05 ***
## PC160 -2.228e-04 3.987e-04 -0.559 0.576332
## PC161 1.258e-04 4.011e-04 0.314 0.753725
## PC162 -1.400e-03 3.982e-04 -3.516 0.000442 ***
## PC163 6.611e-04 4.018e-04 1.645 0.099956 .
## PC164 4.038e-04 4.041e-04 0.999 0.317665
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03162 on 5419 degrees of freedom
## Multiple R-squared: 0.2656, Adjusted R-squared: 0.2434
## F-statistic: 11.95 on 164 and 5419 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 278"
## [1] "Number of data points that have Cook's D > 1: 0"Test
test.model(model.full, data.test
,method = NULL , subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.012 2.088 2.100 2.097 2.110 2.135
## [1] " Test MSE: 0.000991150303789864"
## [1] " Test RMSE: 0.0314825396655013"
## [1] " Test MSE (Org Scale): 89.3211195242851"
## [1] " Test RMSE (Org Scale): 9.4509851086691"
Variable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection with CV
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 128 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03472786 0.0875358 0.02693488 0.001061457 0.01850564 0.0006198120
## 2 2 0.03432460 0.1083901 0.02663880 0.001132797 0.01623561 0.0006639239
## 3 3 0.03382946 0.1348557 0.02626974 0.001208496 0.02748852 0.0008560645
## 4 4 0.03346048 0.1536847 0.02596620 0.001299979 0.03210633 0.0009556136
## 5 5 0.03320182 0.1666182 0.02575696 0.001323985 0.03584527 0.0009502264
## 6 6 0.03301559 0.1760576 0.02560187 0.001332234 0.03751422 0.0009523620
## 7 7 0.03301624 0.1761698 0.02562721 0.001335393 0.03785243 0.0009677117
## 8 8 0.03296990 0.1783994 0.02558746 0.001346942 0.03704331 0.0009257019
## 9 9 0.03287814 0.1829320 0.02551140 0.001356576 0.03677055 0.0008862474
## 10 10 0.03278345 0.1876595 0.02543918 0.001359130 0.03655512 0.0008332271
## 11 11 0.03268174 0.1926185 0.02536312 0.001335263 0.03507154 0.0008276001
## 12 12 0.03253215 0.1998258 0.02525020 0.001349551 0.03526951 0.0008867198
## 13 13 0.03245572 0.2035639 0.02521198 0.001389036 0.03650244 0.0009305479
## 14 14 0.03244631 0.2040401 0.02520276 0.001367673 0.03668919 0.0009118742
## 15 15 0.03240234 0.2061430 0.02517818 0.001364078 0.03711829 0.0008930805
## 16 16 0.03233103 0.2096294 0.02511629 0.001345336 0.03744722 0.0008766231
## 17 17 0.03228304 0.2118675 0.02507836 0.001321496 0.03565761 0.0008792641
## 18 18 0.03224579 0.2137794 0.02504090 0.001324247 0.03512276 0.0008644901
## 19 19 0.03223778 0.2142949 0.02504489 0.001371764 0.03522280 0.0009118315
## 20 20 0.03225900 0.2134128 0.02505024 0.001392853 0.03628137 0.0009265227
## 21 21 0.03225984 0.2133994 0.02505656 0.001418306 0.03686905 0.0009380158
## 22 22 0.03225483 0.2136048 0.02504975 0.001423029 0.03688121 0.0009358668
## 23 23 0.03223728 0.2145096 0.02503852 0.001395590 0.03655494 0.0009290173
## 24 24 0.03222293 0.2151330 0.02504058 0.001387110 0.03599535 0.0009286362
## 25 25 0.03223001 0.2148688 0.02503160 0.001393508 0.03576115 0.0009158367
## 26 26 0.03224018 0.2144694 0.02506042 0.001403107 0.03662796 0.0009210134
## 27 27 0.03230391 0.2116293 0.02512815 0.001391499 0.03640708 0.0009015287
## 28 28 0.03231252 0.2111081 0.02512483 0.001360361 0.03429119 0.0008667704
## 29 29 0.03231213 0.2112150 0.02511799 0.001368343 0.03356237 0.0008617138
## 30 30 0.03229978 0.2118183 0.02511427 0.001368913 0.03314928 0.0008575340
## 31 31 0.03231809 0.2109579 0.02512858 0.001375225 0.03311262 0.0008699165
## 32 32 0.03228285 0.2125278 0.02510698 0.001380127 0.03334608 0.0008777023
## 33 33 0.03228394 0.2125305 0.02510694 0.001391326 0.03364957 0.0008957619
## 34 34 0.03228920 0.2123143 0.02510663 0.001407002 0.03427545 0.0009347894
## 35 35 0.03230975 0.2114299 0.02511794 0.001388391 0.03384686 0.0009227280
## 36 36 0.03231350 0.2112871 0.02514065 0.001363555 0.03272151 0.0009090861
## 37 37 0.03230773 0.2116327 0.02513575 0.001371689 0.03344695 0.0009246265
## 38 38 0.03227340 0.2133739 0.02509772 0.001409556 0.03434243 0.0009382950
## 39 39 0.03225123 0.2143758 0.02509063 0.001390021 0.03313816 0.0009162745
## 40 40 0.03226568 0.2137858 0.02511080 0.001396184 0.03341902 0.0009157467
## 41 41 0.03226115 0.2140337 0.02510319 0.001383636 0.03276791 0.0009161375
## 42 42 0.03224718 0.2146750 0.02509158 0.001373413 0.03149069 0.0009103765
## 43 43 0.03225279 0.2145169 0.02510559 0.001383390 0.03193877 0.0009355992
## 44 44 0.03226071 0.2141930 0.02510978 0.001365292 0.03186572 0.0009245905
## 45 45 0.03227103 0.2137277 0.02510361 0.001343984 0.03078506 0.0008973057
## 46 46 0.03226329 0.2141583 0.02509354 0.001349835 0.03091374 0.0009060144
## 47 47 0.03224825 0.2149717 0.02507693 0.001381468 0.03124203 0.0009103212
## 48 48 0.03224030 0.2154032 0.02506404 0.001371514 0.03102525 0.0009122756
## 49 49 0.03224092 0.2153988 0.02506774 0.001383636 0.03137152 0.0009229711
## 50 50 0.03223536 0.2156435 0.02507311 0.001386541 0.03187797 0.0009344750
## 51 51 0.03221723 0.2164997 0.02505882 0.001379601 0.03137269 0.0009396023
## 52 52 0.03221855 0.2163972 0.02506696 0.001370384 0.03053686 0.0009211003
## 53 53 0.03222420 0.2163134 0.02507088 0.001403175 0.03186734 0.0009512459
## 54 54 0.03222994 0.2161084 0.02508507 0.001410654 0.03188335 0.0009518977
## 55 55 0.03222206 0.2165037 0.02507913 0.001410706 0.03143984 0.0009549478
## 56 56 0.03223218 0.2160596 0.02508843 0.001389879 0.03142599 0.0009304736
## 57 57 0.03223685 0.2158818 0.02509162 0.001401075 0.03175593 0.0009393829
## 58 58 0.03222222 0.2165210 0.02508305 0.001393727 0.03143963 0.0009442923
## 59 59 0.03221799 0.2166564 0.02507939 0.001372242 0.03013502 0.0009172113
## 60 60 0.03221669 0.2167642 0.02507295 0.001374715 0.03000050 0.0009196600
## 61 61 0.03221661 0.2167867 0.02507159 0.001381614 0.03013881 0.0009139894
## 62 62 0.03222103 0.2166722 0.02506765 0.001375603 0.03067475 0.0009077495
## 63 63 0.03222210 0.2166116 0.02506447 0.001371666 0.03089435 0.0009035116
## 64 64 0.03223130 0.2162275 0.02507557 0.001380680 0.03136932 0.0009093219
## 65 65 0.03222903 0.2162698 0.02507441 0.001379088 0.03106330 0.0009147433
## 66 66 0.03222641 0.2164138 0.02507278 0.001387152 0.03118630 0.0009232260
## 67 67 0.03223382 0.2161306 0.02507895 0.001398228 0.03135307 0.0009324173
## 68 68 0.03223264 0.2161592 0.02507292 0.001399229 0.03113678 0.0009264410
## 69 69 0.03223728 0.2159839 0.02507449 0.001392739 0.03058663 0.0009243847
## 70 70 0.03224757 0.2155429 0.02508652 0.001377461 0.02997916 0.0009099068
## 71 71 0.03225153 0.2153364 0.02508926 0.001352171 0.02842819 0.0008933890
## 72 72 0.03225051 0.2153966 0.02509251 0.001350439 0.02822789 0.0008987010
## 73 73 0.03225855 0.2150502 0.02509567 0.001351337 0.02820232 0.0009032594
## 74 74 0.03226159 0.2149529 0.02510132 0.001356721 0.02851973 0.0009080979
## 75 75 0.03225516 0.2152672 0.02508647 0.001351262 0.02834770 0.0008958181
## 76 76 0.03225668 0.2152519 0.02509350 0.001347825 0.02796251 0.0008841565
## 77 77 0.03225032 0.2155653 0.02508864 0.001345113 0.02779111 0.0008791602
## 78 78 0.03224405 0.2158242 0.02508998 0.001347392 0.02774745 0.0008887112
## 79 79 0.03224591 0.2157353 0.02508892 0.001346878 0.02778231 0.0008909226
## 80 80 0.03225200 0.2154778 0.02508832 0.001335942 0.02734292 0.0008748025
## 81 81 0.03225884 0.2151564 0.02509153 0.001324637 0.02718162 0.0008606443
## 82 82 0.03223664 0.2161244 0.02508151 0.001321020 0.02672184 0.0008515260
## 83 83 0.03223795 0.2160876 0.02507995 0.001324246 0.02634207 0.0008562950
## 84 84 0.03223261 0.2163689 0.02507210 0.001328825 0.02651001 0.0008510944
## 85 85 0.03222706 0.2166883 0.02506941 0.001336182 0.02681688 0.0008585041
## 86 86 0.03223055 0.2165903 0.02507377 0.001340014 0.02685902 0.0008620817
## 87 87 0.03223617 0.2163166 0.02508194 0.001345909 0.02712090 0.0008660507
## 88 88 0.03223365 0.2164177 0.02508435 0.001340215 0.02702086 0.0008705548
## 89 89 0.03224057 0.2161300 0.02509227 0.001333299 0.02682158 0.0008550341
## 90 90 0.03223284 0.2165345 0.02508732 0.001325548 0.02651749 0.0008445745
## 91 91 0.03222693 0.2168368 0.02508116 0.001332084 0.02680572 0.0008459608
## 92 92 0.03222574 0.2169262 0.02508015 0.001328645 0.02682913 0.0008395214
## 93 93 0.03221636 0.2173616 0.02506876 0.001323183 0.02667344 0.0008264123
## 94 94 0.03220485 0.2178925 0.02506897 0.001319980 0.02651286 0.0008231077
## 95 95 0.03220880 0.2177585 0.02506687 0.001307583 0.02618915 0.0008193251
## 96 96 0.03221366 0.2176087 0.02506833 0.001313508 0.02625488 0.0008252369
## 97 97 0.03221272 0.2176376 0.02506001 0.001309865 0.02604679 0.0008213999
## 98 98 0.03221363 0.2175647 0.02506078 0.001300335 0.02579463 0.0008143892
## 99 99 0.03221161 0.2176594 0.02505901 0.001291401 0.02556742 0.0008118306
## 100 100 0.03220873 0.2177996 0.02505367 0.001293550 0.02558046 0.0008145242
## 101 101 0.03220823 0.2178479 0.02505088 0.001294739 0.02580925 0.0008167034
## 102 102 0.03220142 0.2181472 0.02504322 0.001291011 0.02581538 0.0008207095
## 103 103 0.03219753 0.2183034 0.02504210 0.001281037 0.02570136 0.0008096457
## 104 104 0.03218424 0.2188754 0.02503180 0.001278422 0.02548358 0.0008085554
## 105 105 0.03218079 0.2190303 0.02503498 0.001280441 0.02557842 0.0008131766
## 106 106 0.03217366 0.2193602 0.02502311 0.001277812 0.02569043 0.0008053023
## 107 107 0.03216809 0.2196252 0.02501704 0.001272877 0.02545116 0.0007951466
## 108 108 0.03216808 0.2196173 0.02501264 0.001263216 0.02492189 0.0007931747
## 109 109 0.03217150 0.2195033 0.02501180 0.001264676 0.02482536 0.0007919822
## 110 110 0.03217206 0.2195015 0.02501112 0.001259099 0.02459067 0.0007822882
## 111 111 0.03217058 0.2195809 0.02500716 0.001258084 0.02467756 0.0007838684
## 112 112 0.03217499 0.2193574 0.02501202 0.001263313 0.02446752 0.0007904589
## 113 113 0.03216557 0.2197871 0.02500514 0.001272334 0.02442241 0.0007981316
## 114 114 0.03215465 0.2202602 0.02500504 0.001271621 0.02442841 0.0007996775
## 115 115 0.03215367 0.2203304 0.02500592 0.001272817 0.02438410 0.0007983731
## 116 116 0.03215459 0.2202785 0.02500770 0.001282036 0.02473138 0.0008021585
## 117 117 0.03215325 0.2203364 0.02500540 0.001289368 0.02477652 0.0008065251
## 118 118 0.03215319 0.2203658 0.02500312 0.001294660 0.02496730 0.0008111401
## 119 119 0.03214747 0.2206024 0.02500386 0.001295849 0.02485580 0.0008146161
## 120 120 0.03214932 0.2205358 0.02500884 0.001294564 0.02489271 0.0008095389
## 121 121 0.03214243 0.2208365 0.02500319 0.001292526 0.02479949 0.0008098072
## 122 122 0.03214673 0.2206589 0.02500628 0.001287106 0.02480052 0.0008030332
## 123 123 0.03214132 0.2208758 0.02499794 0.001289169 0.02496264 0.0008045627
## 124 124 0.03213914 0.2209386 0.02499243 0.001284027 0.02479153 0.0008034610
## 125 125 0.03213497 0.2211229 0.02499164 0.001282096 0.02472662 0.0008024946
## 126 126 0.03213254 0.2212350 0.02499147 0.001284816 0.02460441 0.0008020864
## 127 127 0.03213014 0.2213476 0.02499222 0.001286401 0.02466616 0.0008042794
## 128 128 0.03212743 0.2214716 0.02498858 0.001283676 0.02460828 0.0008032679
## 129 129 0.03213257 0.2212367 0.02499516 0.001283804 0.02476711 0.0008022912
## 130 130 0.03214341 0.2207428 0.02500496 0.001282971 0.02465160 0.0008011337
## 131 131 0.03214361 0.2207392 0.02500632 0.001281660 0.02448111 0.0007980568
## 132 132 0.03214713 0.2205711 0.02501125 0.001288916 0.02459372 0.0008063781
## 133 133 0.03214766 0.2205533 0.02500977 0.001291750 0.02465277 0.0008087701
## 134 134 0.03214920 0.2204811 0.02501350 0.001290373 0.02458310 0.0008093175
## 135 135 0.03214700 0.2205805 0.02501083 0.001289549 0.02470230 0.0008083055
## 136 136 0.03214999 0.2204607 0.02501303 0.001292264 0.02475503 0.0008076937
## 137 137 0.03214770 0.2205711 0.02501255 0.001287982 0.02478240 0.0008057101
## 138 138 0.03215044 0.2204692 0.02501635 0.001293295 0.02506123 0.0008099356
## 139 139 0.03215155 0.2204304 0.02501591 0.001295962 0.02521199 0.0008106315
## 140 140 0.03215290 0.2203795 0.02501696 0.001295249 0.02518937 0.0008124483
## 141 141 0.03215340 0.2203547 0.02501605 0.001293884 0.02524891 0.0008131197
## 142 142 0.03215253 0.2203784 0.02501605 0.001289949 0.02505562 0.0008129935
## 143 143 0.03215481 0.2202736 0.02501811 0.001289495 0.02500553 0.0008140239
## 144 144 0.03215505 0.2202574 0.02501788 0.001290488 0.02505785 0.0008160406
## 145 145 0.03215514 0.2202591 0.02501690 0.001290631 0.02509733 0.0008173932
## 146 146 0.03215442 0.2202897 0.02501649 0.001289807 0.02503932 0.0008162902
## 147 147 0.03215308 0.2203552 0.02501437 0.001291392 0.02504550 0.0008164048
## 148 148 0.03215565 0.2202454 0.02501659 0.001290369 0.02505835 0.0008146290
## 149 149 0.03215570 0.2202458 0.02501654 0.001287929 0.02512666 0.0008120514
## 150 150 0.03215597 0.2202318 0.02501680 0.001288054 0.02512420 0.0008109010
## 151 151 0.03215572 0.2202409 0.02501723 0.001287029 0.02506555 0.0008095030
## 152 152 0.03215683 0.2201922 0.02501802 0.001287265 0.02509710 0.0008107259
## 153 153 0.03215690 0.2201956 0.02501849 0.001286687 0.02504495 0.0008093906
## 154 154 0.03215749 0.2201687 0.02501924 0.001286333 0.02501196 0.0008097988
## 155 155 0.03215804 0.2201430 0.02502004 0.001285163 0.02498089 0.0008088150
## 156 156 0.03215702 0.2201853 0.02501986 0.001284499 0.02498216 0.0008079843
## 157 157 0.03215790 0.2201461 0.02502066 0.001284381 0.02494398 0.0008078590
## 158 158 0.03215845 0.2201212 0.02502071 0.001284343 0.02496558 0.0008072354
## 159 159 0.03215958 0.2200704 0.02502139 0.001283451 0.02492590 0.0008067470
## 160 160 0.03216045 0.2200326 0.02502190 0.001283779 0.02494987 0.0008069686
## 161 161 0.03216010 0.2200481 0.02502137 0.001283490 0.02494464 0.0008067311
## 162 162 0.03216047 0.2200324 0.02502148 0.001283635 0.02496082 0.0008069643
## 163 163 0.03216089 0.2200129 0.02502164 0.001283697 0.02495919 0.0008070398
## 164 164 0.03216074 0.2200205 0.02502151 0.001283672 0.02495766 0.0008069270
## [1] "Best Model"
## nvmax
## 128 128
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096666e+00 2.095837e+00 2.097495e+00
## PC1 -4.994662e-04 -5.720959e-04 -4.268365e-04
## PC2 -9.425799e-04 -1.015893e-03 -8.692666e-04
## PC3 -4.380802e-04 -5.126305e-04 -3.635300e-04
## PC4 -3.246725e-04 -3.998521e-04 -2.494930e-04
## PC5 1.770479e-04 1.003783e-04 2.537174e-04
## PC6 -9.268306e-05 -1.699501e-04 -1.541603e-05
## PC7 -2.083528e-04 -2.875599e-04 -1.291456e-04
## PC8 -4.679908e-05 -1.275351e-04 3.393696e-05
## PC9 -3.953864e-05 -1.216944e-04 4.261715e-05
## PC11 -5.805753e-04 -6.703796e-04 -4.907710e-04
## PC12 -4.672340e-04 -5.618740e-04 -3.725940e-04
## PC13 2.932873e-04 1.968537e-04 3.897208e-04
## PC14 2.350430e-04 1.352257e-04 3.348602e-04
## PC15 -3.860895e-05 -1.400584e-04 6.284055e-05
## PC16 3.066878e-04 2.040967e-04 4.092789e-04
## PC17 -1.706994e-04 -2.788217e-04 -6.257711e-05
## PC18 -3.514516e-04 -4.636688e-04 -2.392344e-04
## PC19 7.473153e-05 -3.939631e-05 1.888594e-04
## PC20 4.099943e-04 2.852873e-04 5.347013e-04
## PC21 1.001202e-04 -2.953939e-05 2.297798e-04
## PC23 2.266011e-04 -2.756836e-05 4.807705e-04
## PC24 -9.051545e-04 -1.198530e-03 -6.117786e-04
## PC25 1.842789e-04 -1.456391e-04 5.141968e-04
## PC26 4.815861e-04 1.461418e-04 8.170304e-04
## PC27 2.351783e-04 -1.078854e-04 5.782421e-04
## PC29 5.606089e-04 1.821783e-04 9.390395e-04
## PC31 -1.757874e-04 -5.876790e-04 2.361042e-04
## PC32 -7.541658e-04 -1.173771e-03 -3.345610e-04
## PC33 4.016172e-04 -2.574890e-05 8.289833e-04
## PC34 1.088889e-03 6.372229e-04 1.540554e-03
## PC37 -5.342118e-04 -1.039450e-03 -2.897305e-05
## PC38 2.857014e-04 -2.412384e-04 8.126412e-04
## PC39 -2.378230e-04 -7.793169e-04 3.036709e-04
## PC40 -2.950903e-04 -8.379358e-04 2.477551e-04
## PC41 -2.650625e-04 -8.223851e-04 2.922602e-04
## PC44 6.332264e-04 6.503779e-05 1.201415e-03
## PC46 1.925968e-04 -3.853919e-04 7.705856e-04
## PC47 -4.971330e-04 -1.073975e-03 7.970891e-05
## PC48 3.294782e-04 -2.470524e-04 9.060088e-04
## PC49 1.935276e-04 -3.962304e-04 7.832857e-04
## PC50 -2.741322e-04 -8.636318e-04 3.153674e-04
## PC51 2.897821e-04 -3.196233e-04 8.991875e-04
## PC52 1.946909e-04 -4.059983e-04 7.953802e-04
## PC54 -3.441852e-04 -9.535152e-04 2.651449e-04
## PC55 -2.032386e-04 -8.151689e-04 4.086917e-04
## PC59 9.442434e-04 3.209480e-04 1.567539e-03
## PC62 -4.282697e-04 -1.054580e-03 1.980405e-04
## PC63 -6.543528e-04 -1.285391e-03 -2.331480e-05
## PC64 -8.919693e-04 -1.528981e-03 -2.549579e-04
## PC66 -3.803545e-04 -1.021367e-03 2.606580e-04
## PC67 3.984130e-04 -2.457885e-04 1.042614e-03
## PC68 8.215906e-04 1.772576e-04 1.465924e-03
## PC69 4.473591e-04 -1.928159e-04 1.087534e-03
## PC71 3.657414e-04 -2.877059e-04 1.019189e-03
## PC73 3.476116e-04 -3.102413e-04 1.005465e-03
## PC74 -4.917876e-04 -1.152889e-03 1.693141e-04
## PC75 -8.658594e-04 -1.518681e-03 -2.130382e-04
## PC76 -3.027718e-04 -9.700648e-04 3.645212e-04
## PC77 4.053651e-04 -2.587483e-04 1.069478e-03
## PC78 1.992840e-04 -4.690350e-04 8.676030e-04
## PC79 6.750569e-04 -3.670558e-06 1.353784e-03
## PC80 -3.706308e-04 -1.046872e-03 3.056106e-04
## PC81 8.730353e-04 1.975549e-04 1.548516e-03
## PC82 2.759786e-04 -4.053389e-04 9.572961e-04
## PC83 -7.355074e-04 -1.417390e-03 -5.362511e-05
## PC84 5.743941e-04 -1.168969e-04 1.265685e-03
## PC85 1.133195e-03 4.438385e-04 1.822551e-03
## PC86 -3.231296e-04 -1.015046e-03 3.687873e-04
## PC87 1.857972e-03 1.167287e-03 2.548657e-03
## PC88 -9.407818e-04 -1.641708e-03 -2.398561e-04
## PC89 -7.229648e-04 -1.428169e-03 -1.776063e-05
## PC90 -9.635388e-04 -1.666450e-03 -2.606281e-04
## PC92 -3.077542e-04 -1.013458e-03 3.979496e-04
## PC93 3.966031e-04 -3.085869e-04 1.101793e-03
## PC94 -6.123031e-04 -1.323448e-03 9.884158e-05
## PC96 -4.638033e-04 -1.179106e-03 2.514997e-04
## PC97 -3.634298e-04 -1.080697e-03 3.538378e-04
## PC98 -5.831352e-04 -1.297566e-03 1.312953e-04
## PC99 -3.844065e-04 -1.103209e-03 3.343960e-04
## PC100 2.564773e-04 -4.608356e-04 9.737901e-04
## PC102 -7.596988e-04 -1.476301e-03 -4.309708e-05
## PC103 5.301392e-04 -1.891829e-04 1.249461e-03
## PC104 -9.053738e-04 -1.625828e-03 -1.849198e-04
## PC105 9.459939e-04 2.240066e-04 1.667981e-03
## PC106 7.122575e-04 -1.442924e-05 1.438944e-03
## PC108 2.550146e-04 -4.702286e-04 9.802577e-04
## PC110 -5.205370e-04 -1.250010e-03 2.089362e-04
## PC111 -5.514555e-04 -1.279101e-03 1.761904e-04
## PC113 2.494954e-04 -4.836280e-04 9.826188e-04
## PC114 -6.702114e-04 -1.399873e-03 5.945026e-05
## PC115 -1.570461e-03 -2.311792e-03 -8.291294e-04
## PC118 3.585688e-04 -3.806879e-04 1.097825e-03
## PC119 -8.729105e-04 -1.614819e-03 -1.310015e-04
## PC120 3.556027e-04 -3.837860e-04 1.094992e-03
## PC121 -4.485811e-04 -1.193258e-03 2.960957e-04
## PC122 6.494122e-04 -9.553612e-05 1.394361e-03
## PC123 -6.919314e-04 -1.434092e-03 5.022948e-05
## PC124 4.738274e-04 -2.701192e-04 1.217774e-03
## PC125 4.893899e-04 -2.629255e-04 1.241705e-03
## PC127 6.656917e-04 -8.093207e-05 1.412315e-03
## PC128 -9.681493e-04 -1.717745e-03 -2.185541e-04
## PC130 2.226598e-04 -5.280043e-04 9.733240e-04
## PC131 -1.136646e-03 -1.892049e-03 -3.812424e-04
## PC132 2.494469e-04 -5.020361e-04 1.000930e-03
## PC134 7.107453e-04 -4.503247e-05 1.466523e-03
## PC135 4.033936e-04 -3.551793e-04 1.161967e-03
## PC136 5.749529e-04 -1.764404e-04 1.326346e-03
## PC137 -2.987741e-04 -1.052349e-03 4.548012e-04
## PC138 3.869480e-04 -3.712815e-04 1.145178e-03
## PC139 -9.131188e-04 -1.673983e-03 -1.522550e-04
## PC140 -4.156647e-04 -1.180406e-03 3.490764e-04
## PC143 3.873471e-04 -3.781969e-04 1.152891e-03
## PC144 7.572249e-04 -5.753474e-06 1.520203e-03
## PC145 3.886415e-04 -3.779249e-04 1.155208e-03
## PC146 7.268788e-04 -4.091190e-05 1.494669e-03
## PC147 -2.663643e-04 -1.039845e-03 5.071162e-04
## PC148 -5.600192e-04 -1.332133e-03 2.120950e-04
## PC150 4.775381e-04 -2.930204e-04 1.248096e-03
## PC151 5.822327e-04 -1.930573e-04 1.357523e-03
## PC152 -5.352598e-04 -1.303381e-03 2.328610e-04
## PC153 8.832533e-04 1.113578e-04 1.655149e-03
## PC154 -1.030280e-03 -1.800222e-03 -2.603387e-04
## PC155 9.879412e-04 2.129936e-04 1.762889e-03
## PC156 5.463272e-04 -2.353111e-04 1.327965e-03
## PC159 1.542246e-03 7.709317e-04 2.313561e-03
## PC162 -1.401950e-03 -2.179824e-03 -6.240774e-04
## PC163 6.723307e-04 -1.122665e-04 1.456928e-03
## PC164 4.072634e-04 -3.814469e-04 1.195974e-03Test
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.011 2.088 2.100 2.097 2.110 2.135
## [1] "leapForward Test MSE: 0.000991528663550522"
## [1] "leapForward Test RMSE: 0.031488548133417"
## [1] "leapForward Test MSE (Org Scale): 89.3559009387407"
## [1] "leapForward Test RMSE (Org Scale): 9.45282502423168"
Backward Elimination with CV
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 128 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03472786 0.0875358 0.02693488 0.001061457 0.01850564 0.0006198120
## 2 2 0.03432460 0.1083901 0.02663880 0.001132797 0.01623561 0.0006639239
## 3 3 0.03382946 0.1348557 0.02626974 0.001208496 0.02748852 0.0008560645
## 4 4 0.03346048 0.1536847 0.02596620 0.001299979 0.03210633 0.0009556136
## 5 5 0.03320182 0.1666182 0.02575696 0.001323985 0.03584527 0.0009502264
## 6 6 0.03301559 0.1760576 0.02560187 0.001332234 0.03751422 0.0009523620
## 7 7 0.03301624 0.1761698 0.02562721 0.001335393 0.03785243 0.0009677117
## 8 8 0.03296990 0.1783994 0.02558746 0.001346942 0.03704331 0.0009257019
## 9 9 0.03287814 0.1829320 0.02551140 0.001356576 0.03677055 0.0008862474
## 10 10 0.03278345 0.1876595 0.02543918 0.001359130 0.03655512 0.0008332271
## 11 11 0.03268174 0.1926185 0.02536312 0.001335263 0.03507154 0.0008276001
## 12 12 0.03253215 0.1998258 0.02525020 0.001349551 0.03526951 0.0008867198
## 13 13 0.03245572 0.2035639 0.02521198 0.001389036 0.03650244 0.0009305479
## 14 14 0.03244559 0.2040930 0.02520042 0.001368563 0.03673819 0.0009141766
## 15 15 0.03240668 0.2059316 0.02517003 0.001358784 0.03693702 0.0009010627
## 16 16 0.03233103 0.2096294 0.02511629 0.001345336 0.03744722 0.0008766231
## 17 17 0.03228304 0.2118675 0.02507836 0.001321496 0.03565761 0.0008792641
## 18 18 0.03224579 0.2137794 0.02504090 0.001324247 0.03512276 0.0008644901
## 19 19 0.03223778 0.2142949 0.02504489 0.001371764 0.03522280 0.0009118315
## 20 20 0.03225900 0.2134128 0.02505024 0.001392853 0.03628137 0.0009265227
## 21 21 0.03225984 0.2133994 0.02505656 0.001418306 0.03686905 0.0009380158
## 22 22 0.03225483 0.2136048 0.02504975 0.001423029 0.03688121 0.0009358668
## 23 23 0.03223728 0.2145096 0.02503852 0.001395590 0.03655494 0.0009290173
## 24 24 0.03222293 0.2151330 0.02504058 0.001387110 0.03599535 0.0009286362
## 25 25 0.03223955 0.2143852 0.02503578 0.001388714 0.03525752 0.0009256415
## 26 26 0.03225127 0.2137937 0.02505803 0.001392841 0.03528662 0.0009391822
## 27 27 0.03230478 0.2114412 0.02511543 0.001374739 0.03504477 0.0009089633
## 28 28 0.03231252 0.2111081 0.02512483 0.001360361 0.03429119 0.0008667704
## 29 29 0.03231090 0.2112681 0.02511968 0.001365963 0.03355562 0.0008640029
## 30 30 0.03229964 0.2118244 0.02511935 0.001368649 0.03314820 0.0008645148
## 31 31 0.03231195 0.2112430 0.02512057 0.001363347 0.03307288 0.0008593860
## 32 32 0.03228285 0.2125278 0.02510698 0.001380127 0.03334608 0.0008777023
## 33 33 0.03228199 0.2126287 0.02510763 0.001391727 0.03367655 0.0008956465
## 34 34 0.03229478 0.2121431 0.02511947 0.001414980 0.03482179 0.0009383104
## 35 35 0.03230763 0.2115287 0.02511912 0.001386249 0.03365635 0.0009231052
## 36 36 0.03231790 0.2110682 0.02514218 0.001358079 0.03250379 0.0009073367
## 37 37 0.03230719 0.2116561 0.02513643 0.001372360 0.03346998 0.0009238903
## 38 38 0.03227255 0.2134134 0.02509780 0.001410602 0.03438104 0.0009382064
## 39 39 0.03225123 0.2143758 0.02509063 0.001390021 0.03313816 0.0009162745
## 40 40 0.03226568 0.2137858 0.02511080 0.001396184 0.03341902 0.0009157467
## 41 41 0.03226115 0.2140337 0.02510319 0.001383636 0.03276791 0.0009161375
## 42 42 0.03224718 0.2146750 0.02509158 0.001373413 0.03149069 0.0009103765
## 43 43 0.03225382 0.2144627 0.02510299 0.001383821 0.03200384 0.0009336970
## 44 44 0.03225800 0.2143041 0.02510986 0.001364040 0.03172435 0.0009246468
## 45 45 0.03226723 0.2138959 0.02510620 0.001342333 0.03057449 0.0008992983
## 46 46 0.03227014 0.2138208 0.02510468 0.001340406 0.03047724 0.0008914093
## 47 47 0.03225285 0.2147433 0.02508381 0.001375393 0.03096309 0.0009017271
## 48 48 0.03224360 0.2152433 0.02506689 0.001367153 0.03083078 0.0009087694
## 49 49 0.03223889 0.2154361 0.02506941 0.001371442 0.03124355 0.0009129428
## 50 50 0.03222749 0.2159614 0.02507009 0.001382848 0.03215921 0.0009317858
## 51 51 0.03222963 0.2159458 0.02505835 0.001397738 0.03249610 0.0009460428
## 52 52 0.03223383 0.2157654 0.02506939 0.001378619 0.03156287 0.0009268465
## 53 53 0.03222863 0.2161335 0.02506729 0.001395336 0.03140917 0.0009439818
## 54 54 0.03224000 0.2155985 0.02509211 0.001393918 0.03099899 0.0009388780
## 55 55 0.03223418 0.2159090 0.02509074 0.001393878 0.03059475 0.0009394035
## 56 56 0.03223218 0.2160596 0.02508843 0.001389879 0.03142599 0.0009304736
## 57 57 0.03223685 0.2158818 0.02509162 0.001401075 0.03175593 0.0009393829
## 58 58 0.03222222 0.2165210 0.02508305 0.001393727 0.03143963 0.0009442923
## 59 59 0.03221799 0.2166564 0.02507939 0.001372242 0.03013502 0.0009172113
## 60 60 0.03221669 0.2167642 0.02507295 0.001374715 0.03000050 0.0009196600
## 61 61 0.03221677 0.2167911 0.02507291 0.001381743 0.03013083 0.0009142891
## 62 62 0.03222116 0.2166776 0.02506941 0.001375715 0.03066510 0.0009081686
## 63 63 0.03221341 0.2169443 0.02505759 0.001369270 0.03062542 0.0009026209
## 64 64 0.03221405 0.2169562 0.02505627 0.001378549 0.03098307 0.0009133733
## 65 65 0.03220829 0.2172380 0.02506142 0.001383679 0.03128122 0.0009094501
## 66 66 0.03221224 0.2170640 0.02507370 0.001392166 0.03176027 0.0009182890
## 67 67 0.03222483 0.2165418 0.02507240 0.001396771 0.03131751 0.0009263191
## 68 68 0.03223364 0.2161190 0.02507534 0.001385673 0.03068932 0.0009133469
## 69 69 0.03222927 0.2163435 0.02506639 0.001386312 0.03066340 0.0009157411
## 70 70 0.03224415 0.2156983 0.02508324 0.001376796 0.03007614 0.0009073967
## 71 71 0.03224721 0.2155414 0.02508778 0.001353251 0.02907374 0.0008935575
## 72 72 0.03225711 0.2151036 0.02509757 0.001354142 0.02869893 0.0009040082
## 73 73 0.03226097 0.2149462 0.02509788 0.001352647 0.02836661 0.0009055452
## 74 74 0.03226159 0.2149529 0.02510132 0.001356721 0.02851973 0.0009080979
## 75 75 0.03225516 0.2152672 0.02508647 0.001351262 0.02834770 0.0008958181
## 76 76 0.03225668 0.2152519 0.02509350 0.001347825 0.02796251 0.0008841565
## 77 77 0.03224701 0.2157146 0.02508491 0.001348569 0.02783423 0.0008838746
## 78 78 0.03224611 0.2157297 0.02508961 0.001345250 0.02772145 0.0008891721
## 79 79 0.03224718 0.2156710 0.02509066 0.001344065 0.02778413 0.0008879319
## 80 80 0.03224682 0.2156896 0.02508690 0.001330162 0.02721748 0.0008700918
## 81 81 0.03225201 0.2154492 0.02508904 0.001322023 0.02705390 0.0008582655
## 82 82 0.03223664 0.2161244 0.02508151 0.001321020 0.02672184 0.0008515260
## 83 83 0.03223795 0.2160876 0.02507995 0.001324246 0.02634207 0.0008562950
## 84 84 0.03222582 0.2166659 0.02506513 0.001336274 0.02662730 0.0008604205
## 85 85 0.03222020 0.2169892 0.02506240 0.001343909 0.02695894 0.0008683547
## 86 86 0.03223055 0.2165903 0.02507377 0.001340014 0.02685902 0.0008620817
## 87 87 0.03223461 0.2163825 0.02507872 0.001342431 0.02706857 0.0008599609
## 88 88 0.03223209 0.2164836 0.02508119 0.001336719 0.02696744 0.0008644918
## 89 89 0.03223967 0.2161828 0.02509126 0.001332700 0.02680514 0.0008544575
## 90 90 0.03223344 0.2165079 0.02508525 0.001332197 0.02659987 0.0008488020
## 91 91 0.03222412 0.2169634 0.02508246 0.001334837 0.02684114 0.0008473485
## 92 92 0.03222305 0.2170220 0.02507983 0.001324039 0.02674285 0.0008337366
## 93 93 0.03221207 0.2175078 0.02507154 0.001316332 0.02645838 0.0008219883
## 94 94 0.03220971 0.2176728 0.02507283 0.001317391 0.02638679 0.0008254195
## 95 95 0.03220782 0.2177521 0.02506350 0.001305749 0.02614404 0.0008216708
## 96 96 0.03221175 0.2176451 0.02506563 0.001312648 0.02622361 0.0008256128
## 97 97 0.03221257 0.2176173 0.02506029 0.001308958 0.02599153 0.0008213930
## 98 98 0.03221818 0.2173602 0.02506236 0.001299372 0.02585117 0.0008148330
## 99 99 0.03221343 0.2175901 0.02505882 0.001289086 0.02545936 0.0008121033
## 100 100 0.03220681 0.2178967 0.02504888 0.001295972 0.02572929 0.0008214924
## 101 101 0.03220694 0.2179238 0.02504739 0.001296372 0.02592640 0.0008218492
## 102 102 0.03220142 0.2181472 0.02504322 0.001291011 0.02581538 0.0008207095
## 103 103 0.03219913 0.2182395 0.02503982 0.001280353 0.02570214 0.0008091609
## 104 104 0.03218508 0.2188446 0.02502872 0.001278065 0.02548428 0.0008078740
## 105 105 0.03218194 0.2189944 0.02503384 0.001278751 0.02549264 0.0008111746
## 106 106 0.03217566 0.2192707 0.02502626 0.001275268 0.02555473 0.0008007975
## 107 107 0.03216809 0.2196252 0.02501704 0.001272877 0.02545116 0.0007951466
## 108 108 0.03216808 0.2196173 0.02501264 0.001263216 0.02492189 0.0007931747
## 109 109 0.03217144 0.2195066 0.02501127 0.001264540 0.02482304 0.0007909065
## 110 110 0.03217519 0.2193623 0.02501282 0.001266321 0.02469393 0.0007857961
## 111 111 0.03217768 0.2192832 0.02501277 0.001274485 0.02490235 0.0007953831
## 112 112 0.03217897 0.2191993 0.02501609 0.001272554 0.02459325 0.0007988454
## 113 113 0.03216557 0.2197871 0.02500514 0.001272334 0.02442241 0.0007981316
## 114 114 0.03215465 0.2202602 0.02500504 0.001271621 0.02442841 0.0007996775
## 115 115 0.03215142 0.2204364 0.02500535 0.001272517 0.02448294 0.0007979897
## 116 116 0.03215236 0.2203834 0.02500719 0.001281701 0.02482331 0.0008018124
## 117 117 0.03215337 0.2203307 0.02500597 0.001289385 0.02477153 0.0008069133
## 118 118 0.03215319 0.2203658 0.02500312 0.001294660 0.02496730 0.0008111401
## 119 119 0.03214747 0.2206024 0.02500386 0.001295849 0.02485580 0.0008146161
## 120 120 0.03214932 0.2205358 0.02500884 0.001294564 0.02489271 0.0008095389
## 121 121 0.03214435 0.2207464 0.02500319 0.001292875 0.02472779 0.0008098091
## 122 122 0.03214769 0.2206137 0.02500441 0.001287279 0.02476441 0.0008017226
## 123 123 0.03214328 0.2207841 0.02499782 0.001289532 0.02489074 0.0008044744
## 124 124 0.03213914 0.2209386 0.02499243 0.001284027 0.02479153 0.0008034610
## 125 125 0.03213497 0.2211229 0.02499164 0.001282096 0.02472662 0.0008024946
## 126 126 0.03213254 0.2212350 0.02499147 0.001284816 0.02460441 0.0008020864
## 127 127 0.03213014 0.2213476 0.02499222 0.001286401 0.02466616 0.0008042794
## 128 128 0.03212743 0.2214716 0.02498858 0.001283676 0.02460828 0.0008032679
## 129 129 0.03213257 0.2212367 0.02499516 0.001283804 0.02476711 0.0008022912
## 130 130 0.03214341 0.2207428 0.02500496 0.001282971 0.02465160 0.0008011337
## 131 131 0.03214361 0.2207392 0.02500632 0.001281660 0.02448111 0.0007980568
## 132 132 0.03214713 0.2205711 0.02501125 0.001288916 0.02459372 0.0008063781
## 133 133 0.03214766 0.2205533 0.02500977 0.001291750 0.02465277 0.0008087701
## 134 134 0.03214920 0.2204811 0.02501350 0.001290373 0.02458310 0.0008093175
## 135 135 0.03214700 0.2205805 0.02501083 0.001289549 0.02470230 0.0008083055
## 136 136 0.03214999 0.2204607 0.02501303 0.001292264 0.02475503 0.0008076937
## 137 137 0.03214770 0.2205711 0.02501255 0.001287982 0.02478240 0.0008057101
## 138 138 0.03215044 0.2204692 0.02501635 0.001293295 0.02506123 0.0008099356
## 139 139 0.03215155 0.2204304 0.02501591 0.001295962 0.02521199 0.0008106315
## 140 140 0.03215407 0.2203298 0.02501793 0.001295102 0.02522243 0.0008115628
## 141 141 0.03215314 0.2203683 0.02501707 0.001293967 0.02524324 0.0008118590
## 142 142 0.03215253 0.2203784 0.02501605 0.001289949 0.02505562 0.0008129935
## 143 143 0.03215481 0.2202736 0.02501811 0.001289495 0.02500553 0.0008140239
## 144 144 0.03215505 0.2202574 0.02501788 0.001290488 0.02505785 0.0008160406
## 145 145 0.03215514 0.2202591 0.02501690 0.001290631 0.02509733 0.0008173932
## 146 146 0.03215442 0.2202897 0.02501649 0.001289807 0.02503932 0.0008162902
## 147 147 0.03215308 0.2203552 0.02501437 0.001291392 0.02504550 0.0008164048
## 148 148 0.03215565 0.2202454 0.02501659 0.001290369 0.02505835 0.0008146290
## 149 149 0.03215570 0.2202458 0.02501654 0.001287929 0.02512666 0.0008120514
## 150 150 0.03215597 0.2202318 0.02501680 0.001288054 0.02512420 0.0008109010
## 151 151 0.03215572 0.2202409 0.02501723 0.001287029 0.02506555 0.0008095030
## 152 152 0.03215683 0.2201922 0.02501802 0.001287265 0.02509710 0.0008107259
## 153 153 0.03215690 0.2201956 0.02501849 0.001286687 0.02504495 0.0008093906
## 154 154 0.03215749 0.2201687 0.02501924 0.001286333 0.02501196 0.0008097988
## 155 155 0.03215804 0.2201430 0.02502004 0.001285163 0.02498089 0.0008088150
## 156 156 0.03215702 0.2201853 0.02501986 0.001284499 0.02498216 0.0008079843
## 157 157 0.03215790 0.2201461 0.02502066 0.001284381 0.02494398 0.0008078590
## 158 158 0.03215845 0.2201212 0.02502071 0.001284343 0.02496558 0.0008072354
## 159 159 0.03215958 0.2200704 0.02502139 0.001283451 0.02492590 0.0008067470
## 160 160 0.03216045 0.2200326 0.02502190 0.001283779 0.02494987 0.0008069686
## 161 161 0.03216010 0.2200481 0.02502137 0.001283490 0.02494464 0.0008067311
## 162 162 0.03216047 0.2200324 0.02502148 0.001283635 0.02496082 0.0008069643
## 163 163 0.03216089 0.2200129 0.02502164 0.001283697 0.02495919 0.0008070398
## 164 164 0.03216074 0.2200205 0.02502151 0.001283672 0.02495766 0.0008069270
## [1] "Best Model"
## nvmax
## 128 128
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096666e+00 2.095837e+00 2.097495e+00
## PC1 -4.994662e-04 -5.720959e-04 -4.268365e-04
## PC2 -9.425799e-04 -1.015893e-03 -8.692666e-04
## PC3 -4.380802e-04 -5.126305e-04 -3.635300e-04
## PC4 -3.246725e-04 -3.998521e-04 -2.494930e-04
## PC5 1.770479e-04 1.003783e-04 2.537174e-04
## PC6 -9.268306e-05 -1.699501e-04 -1.541603e-05
## PC7 -2.083528e-04 -2.875599e-04 -1.291456e-04
## PC8 -4.679908e-05 -1.275351e-04 3.393696e-05
## PC9 -3.953864e-05 -1.216944e-04 4.261715e-05
## PC11 -5.805753e-04 -6.703796e-04 -4.907710e-04
## PC12 -4.672340e-04 -5.618740e-04 -3.725940e-04
## PC13 2.932873e-04 1.968537e-04 3.897208e-04
## PC14 2.350430e-04 1.352257e-04 3.348602e-04
## PC15 -3.860895e-05 -1.400584e-04 6.284055e-05
## PC16 3.066878e-04 2.040967e-04 4.092789e-04
## PC17 -1.706994e-04 -2.788217e-04 -6.257711e-05
## PC18 -3.514516e-04 -4.636688e-04 -2.392344e-04
## PC19 7.473153e-05 -3.939631e-05 1.888594e-04
## PC20 4.099943e-04 2.852873e-04 5.347013e-04
## PC21 1.001202e-04 -2.953939e-05 2.297798e-04
## PC23 2.266011e-04 -2.756836e-05 4.807705e-04
## PC24 -9.051545e-04 -1.198530e-03 -6.117786e-04
## PC25 1.842789e-04 -1.456391e-04 5.141968e-04
## PC26 4.815861e-04 1.461418e-04 8.170304e-04
## PC27 2.351783e-04 -1.078854e-04 5.782421e-04
## PC29 5.606089e-04 1.821783e-04 9.390395e-04
## PC31 -1.757874e-04 -5.876790e-04 2.361042e-04
## PC32 -7.541658e-04 -1.173771e-03 -3.345610e-04
## PC33 4.016172e-04 -2.574890e-05 8.289833e-04
## PC34 1.088889e-03 6.372229e-04 1.540554e-03
## PC37 -5.342118e-04 -1.039450e-03 -2.897305e-05
## PC38 2.857014e-04 -2.412384e-04 8.126412e-04
## PC39 -2.378230e-04 -7.793169e-04 3.036709e-04
## PC40 -2.950903e-04 -8.379358e-04 2.477551e-04
## PC41 -2.650625e-04 -8.223851e-04 2.922602e-04
## PC44 6.332264e-04 6.503779e-05 1.201415e-03
## PC46 1.925968e-04 -3.853919e-04 7.705856e-04
## PC47 -4.971330e-04 -1.073975e-03 7.970891e-05
## PC48 3.294782e-04 -2.470524e-04 9.060088e-04
## PC49 1.935276e-04 -3.962304e-04 7.832857e-04
## PC50 -2.741322e-04 -8.636318e-04 3.153674e-04
## PC51 2.897821e-04 -3.196233e-04 8.991875e-04
## PC52 1.946909e-04 -4.059983e-04 7.953802e-04
## PC54 -3.441852e-04 -9.535152e-04 2.651449e-04
## PC55 -2.032386e-04 -8.151689e-04 4.086917e-04
## PC59 9.442434e-04 3.209480e-04 1.567539e-03
## PC62 -4.282697e-04 -1.054580e-03 1.980405e-04
## PC63 -6.543528e-04 -1.285391e-03 -2.331480e-05
## PC64 -8.919693e-04 -1.528981e-03 -2.549579e-04
## PC66 -3.803545e-04 -1.021367e-03 2.606580e-04
## PC67 3.984130e-04 -2.457885e-04 1.042614e-03
## PC68 8.215906e-04 1.772576e-04 1.465924e-03
## PC69 4.473591e-04 -1.928159e-04 1.087534e-03
## PC71 3.657414e-04 -2.877059e-04 1.019189e-03
## PC73 3.476116e-04 -3.102413e-04 1.005465e-03
## PC74 -4.917876e-04 -1.152889e-03 1.693141e-04
## PC75 -8.658594e-04 -1.518681e-03 -2.130382e-04
## PC76 -3.027718e-04 -9.700648e-04 3.645212e-04
## PC77 4.053651e-04 -2.587483e-04 1.069478e-03
## PC78 1.992840e-04 -4.690350e-04 8.676030e-04
## PC79 6.750569e-04 -3.670558e-06 1.353784e-03
## PC80 -3.706308e-04 -1.046872e-03 3.056106e-04
## PC81 8.730353e-04 1.975549e-04 1.548516e-03
## PC82 2.759786e-04 -4.053389e-04 9.572961e-04
## PC83 -7.355074e-04 -1.417390e-03 -5.362511e-05
## PC84 5.743941e-04 -1.168969e-04 1.265685e-03
## PC85 1.133195e-03 4.438385e-04 1.822551e-03
## PC86 -3.231296e-04 -1.015046e-03 3.687873e-04
## PC87 1.857972e-03 1.167287e-03 2.548657e-03
## PC88 -9.407818e-04 -1.641708e-03 -2.398561e-04
## PC89 -7.229648e-04 -1.428169e-03 -1.776063e-05
## PC90 -9.635388e-04 -1.666450e-03 -2.606281e-04
## PC92 -3.077542e-04 -1.013458e-03 3.979496e-04
## PC93 3.966031e-04 -3.085869e-04 1.101793e-03
## PC94 -6.123031e-04 -1.323448e-03 9.884158e-05
## PC96 -4.638033e-04 -1.179106e-03 2.514997e-04
## PC97 -3.634298e-04 -1.080697e-03 3.538378e-04
## PC98 -5.831352e-04 -1.297566e-03 1.312953e-04
## PC99 -3.844065e-04 -1.103209e-03 3.343960e-04
## PC100 2.564773e-04 -4.608356e-04 9.737901e-04
## PC102 -7.596988e-04 -1.476301e-03 -4.309708e-05
## PC103 5.301392e-04 -1.891829e-04 1.249461e-03
## PC104 -9.053738e-04 -1.625828e-03 -1.849198e-04
## PC105 9.459939e-04 2.240066e-04 1.667981e-03
## PC106 7.122575e-04 -1.442924e-05 1.438944e-03
## PC108 2.550146e-04 -4.702286e-04 9.802577e-04
## PC110 -5.205370e-04 -1.250010e-03 2.089362e-04
## PC111 -5.514555e-04 -1.279101e-03 1.761904e-04
## PC113 2.494954e-04 -4.836280e-04 9.826188e-04
## PC114 -6.702114e-04 -1.399873e-03 5.945026e-05
## PC115 -1.570461e-03 -2.311792e-03 -8.291294e-04
## PC118 3.585688e-04 -3.806879e-04 1.097825e-03
## PC119 -8.729105e-04 -1.614819e-03 -1.310015e-04
## PC120 3.556027e-04 -3.837860e-04 1.094992e-03
## PC121 -4.485811e-04 -1.193258e-03 2.960957e-04
## PC122 6.494122e-04 -9.553612e-05 1.394361e-03
## PC123 -6.919314e-04 -1.434092e-03 5.022948e-05
## PC124 4.738274e-04 -2.701192e-04 1.217774e-03
## PC125 4.893899e-04 -2.629255e-04 1.241705e-03
## PC127 6.656917e-04 -8.093207e-05 1.412315e-03
## PC128 -9.681493e-04 -1.717745e-03 -2.185541e-04
## PC130 2.226598e-04 -5.280043e-04 9.733240e-04
## PC131 -1.136646e-03 -1.892049e-03 -3.812424e-04
## PC132 2.494469e-04 -5.020361e-04 1.000930e-03
## PC134 7.107453e-04 -4.503247e-05 1.466523e-03
## PC135 4.033936e-04 -3.551793e-04 1.161967e-03
## PC136 5.749529e-04 -1.764404e-04 1.326346e-03
## PC137 -2.987741e-04 -1.052349e-03 4.548012e-04
## PC138 3.869480e-04 -3.712815e-04 1.145178e-03
## PC139 -9.131188e-04 -1.673983e-03 -1.522550e-04
## PC140 -4.156647e-04 -1.180406e-03 3.490764e-04
## PC143 3.873471e-04 -3.781969e-04 1.152891e-03
## PC144 7.572249e-04 -5.753474e-06 1.520203e-03
## PC145 3.886415e-04 -3.779249e-04 1.155208e-03
## PC146 7.268788e-04 -4.091190e-05 1.494669e-03
## PC147 -2.663643e-04 -1.039845e-03 5.071162e-04
## PC148 -5.600192e-04 -1.332133e-03 2.120950e-04
## PC150 4.775381e-04 -2.930204e-04 1.248096e-03
## PC151 5.822327e-04 -1.930573e-04 1.357523e-03
## PC152 -5.352598e-04 -1.303381e-03 2.328610e-04
## PC153 8.832533e-04 1.113578e-04 1.655149e-03
## PC154 -1.030280e-03 -1.800222e-03 -2.603387e-04
## PC155 9.879412e-04 2.129936e-04 1.762889e-03
## PC156 5.463272e-04 -2.353111e-04 1.327965e-03
## PC159 1.542246e-03 7.709317e-04 2.313561e-03
## PC162 -1.401950e-03 -2.179824e-03 -6.240774e-04
## PC163 6.723307e-04 -1.122665e-04 1.456928e-03
## PC164 4.072634e-04 -3.814469e-04 1.195974e-03Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.011 2.088 2.100 2.097 2.110 2.135
## [1] "leapBackward Test MSE: 0.000991528663550521"
## [1] "leapBackward Test RMSE: 0.031488548133417"
## [1] "leapBackward Test MSE (Org Scale): 89.3559009387407"
## [1] "leapBackward Test RMSE (Org Scale): 9.45282502423168"
Stepwise Selection with CV
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 124 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03472786 0.0875358 0.02693488 0.001061457 0.01850564 0.0006198120
## 2 2 0.03432460 0.1083901 0.02663880 0.001132797 0.01623561 0.0006639239
## 3 3 0.03381950 0.1354576 0.02626943 0.001207490 0.02812201 0.0008561529
## 4 4 0.03371671 0.1400011 0.02616103 0.001175280 0.02553747 0.0007177831
## 5 5 0.03320182 0.1666182 0.02575696 0.001323985 0.03584527 0.0009502264
## 6 6 0.03366187 0.1428485 0.02612199 0.001199574 0.02643690 0.0007409604
## 7 7 0.03301624 0.1761698 0.02562721 0.001335393 0.03785243 0.0009677117
## 8 8 0.03296990 0.1783994 0.02558746 0.001346942 0.03704331 0.0009257019
## 9 9 0.03287814 0.1829320 0.02551140 0.001356576 0.03677055 0.0008862474
## 10 10 0.03278345 0.1876595 0.02543918 0.001359130 0.03655512 0.0008332271
## 11 11 0.03268174 0.1926185 0.02536312 0.001335263 0.03507154 0.0008276001
## 12 12 0.03253215 0.1998258 0.02525020 0.001349551 0.03526951 0.0008867198
## 13 13 0.03252973 0.1998886 0.02527522 0.001464999 0.03897408 0.0010061012
## 14 14 0.03249943 0.2014364 0.02526179 0.001278920 0.03140575 0.0007976783
## 15 15 0.03240610 0.2056590 0.02514527 0.001358204 0.03743793 0.0008940452
## 16 16 0.03250450 0.2010763 0.02524551 0.001286826 0.03953483 0.0009060775
## 17 17 0.03229531 0.2112959 0.02509286 0.001327139 0.03562518 0.0008811913
## 18 18 0.03229176 0.2115476 0.02505879 0.001349441 0.03518790 0.0008803835
## 19 19 0.03223778 0.2142949 0.02504489 0.001371764 0.03522280 0.0009118315
## 20 20 0.03225900 0.2134128 0.02505024 0.001392853 0.03628137 0.0009265227
## 21 21 0.03230060 0.2114551 0.02508710 0.001414429 0.03789628 0.0009606040
## 22 22 0.03225483 0.2136048 0.02504975 0.001423029 0.03688121 0.0009358668
## 23 23 0.03223728 0.2145096 0.02503852 0.001395590 0.03655494 0.0009290173
## 24 24 0.03222293 0.2151330 0.02504058 0.001387110 0.03599535 0.0009286362
## 25 25 0.03223001 0.2148688 0.02503160 0.001393508 0.03576115 0.0009158367
## 26 26 0.03220896 0.2154488 0.02503766 0.001371542 0.03478436 0.0009138839
## 27 27 0.03230478 0.2114412 0.02511543 0.001374739 0.03504477 0.0009089633
## 28 28 0.03226995 0.2128408 0.02509219 0.001326659 0.03312001 0.0008005138
## 29 29 0.03231513 0.2109202 0.02512707 0.001368084 0.03355449 0.0008622217
## 30 30 0.03228440 0.2127970 0.02512507 0.001394761 0.03525297 0.0008526558
## 31 31 0.03233203 0.2101810 0.02513962 0.001343610 0.03298332 0.0008405545
## 32 32 0.03229833 0.2117652 0.02513227 0.001410672 0.03356360 0.0009126150
## 33 33 0.03228394 0.2125305 0.02510694 0.001391326 0.03364957 0.0008957619
## 34 34 0.03228736 0.2124084 0.02510701 0.001407550 0.03431740 0.0009346640
## 35 35 0.03233000 0.2104103 0.02514800 0.001380777 0.03328631 0.0009174022
## 36 36 0.03227811 0.2123645 0.02510663 0.001327187 0.03092459 0.0008960529
## 37 37 0.03231721 0.2110141 0.02513455 0.001376730 0.03341905 0.0009234672
## 38 38 0.03227072 0.2133136 0.02510010 0.001409603 0.03451903 0.0009404868
## 39 39 0.03222710 0.2156048 0.02502507 0.001355812 0.03316403 0.0008697535
## 40 40 0.03226568 0.2137858 0.02511080 0.001396184 0.03341902 0.0009157467
## 41 41 0.03226115 0.2140337 0.02510319 0.001383636 0.03276791 0.0009161375
## 42 42 0.03224718 0.2146750 0.02509158 0.001373413 0.03149069 0.0009103765
## 43 43 0.03225279 0.2145169 0.02510559 0.001383390 0.03193877 0.0009355992
## 44 44 0.03226071 0.2141930 0.02510978 0.001365292 0.03186572 0.0009245905
## 45 45 0.03226723 0.2138959 0.02510620 0.001342333 0.03057449 0.0008992983
## 46 46 0.03230253 0.2120542 0.02512238 0.001308309 0.02967677 0.0008953525
## 47 47 0.03224825 0.2149717 0.02507693 0.001381468 0.03124203 0.0009103212
## 48 48 0.03224403 0.2150374 0.02504876 0.001391638 0.03162426 0.0009171055
## 49 49 0.03227280 0.2138357 0.02507883 0.001343688 0.02970460 0.0009095567
## 50 50 0.03223751 0.2155493 0.02507678 0.001386026 0.03208745 0.0009322012
## 51 51 0.03228722 0.2129211 0.02509804 0.001319199 0.02983498 0.0008974471
## 52 52 0.03225393 0.2140078 0.02507760 0.001376698 0.03289270 0.0009353513
## 53 53 0.03223154 0.2157774 0.02507395 0.001407203 0.03270860 0.0009575115
## 54 54 0.03222911 0.2158386 0.02507144 0.001412416 0.03186882 0.0009475879
## 55 55 0.03227204 0.2138252 0.02512724 0.001396276 0.03234816 0.0009610069
## 56 56 0.03228798 0.2133170 0.02512033 0.001320157 0.02854438 0.0008910529
## 57 57 0.03223685 0.2158818 0.02509162 0.001401075 0.03175593 0.0009393829
## 58 58 0.03219196 0.2181133 0.02507690 0.001440836 0.03457068 0.0009553004
## 59 59 0.03221799 0.2166564 0.02507939 0.001372242 0.03013502 0.0009172113
## 60 60 0.03221669 0.2167642 0.02507295 0.001374715 0.03000050 0.0009196600
## 61 61 0.03225340 0.2149917 0.02510926 0.001368754 0.03040195 0.0009227780
## 62 62 0.03221129 0.2164783 0.02504541 0.001367416 0.03102646 0.0009054078
## 63 63 0.03222210 0.2166116 0.02506447 0.001371666 0.03089435 0.0009035116
## 64 64 0.03223130 0.2162275 0.02507557 0.001380680 0.03136932 0.0009093219
## 65 65 0.03222717 0.2158354 0.02506739 0.001376079 0.03074262 0.0009102436
## 66 66 0.03220459 0.2165475 0.02504843 0.001378992 0.03151796 0.0009165683
## 67 67 0.03226061 0.2147647 0.02508997 0.001361375 0.02984281 0.0009185034
## 68 68 0.03224399 0.2154627 0.02508587 0.001395886 0.03167679 0.0009261175
## 69 69 0.03222927 0.2163435 0.02506639 0.001386312 0.03066340 0.0009157411
## 70 70 0.03223867 0.2159915 0.02504534 0.001379445 0.03049528 0.0008754413
## 71 71 0.03224229 0.2157628 0.02508307 0.001350448 0.02871918 0.0008885700
## 72 72 0.03225051 0.2153966 0.02509251 0.001350439 0.02822789 0.0008987010
## 73 73 0.03226097 0.2149462 0.02509788 0.001352647 0.02836661 0.0009055452
## 74 74 0.03228380 0.2137342 0.02511879 0.001370527 0.03061685 0.0009279178
## 75 75 0.03225516 0.2152672 0.02508647 0.001351262 0.02834770 0.0008958181
## 76 76 0.03224645 0.2157971 0.02506158 0.001346003 0.02835528 0.0008638423
## 77 77 0.03228916 0.2134331 0.02512612 0.001310121 0.02804879 0.0008394870
## 78 78 0.03224405 0.2158242 0.02508998 0.001347392 0.02774745 0.0008887112
## 79 79 0.03223243 0.2164450 0.02505827 0.001340628 0.02836758 0.0008667642
## 80 80 0.03224829 0.2156470 0.02508529 0.001338391 0.02742150 0.0008779441
## 81 81 0.03225201 0.2154492 0.02508904 0.001322023 0.02705390 0.0008582655
## 82 82 0.03228553 0.2134602 0.02512285 0.001295640 0.02980780 0.0008171127
## 83 83 0.03226327 0.2147610 0.02510441 0.001339374 0.02868908 0.0008821531
## 84 84 0.03224074 0.2159390 0.02508436 0.001347345 0.02690431 0.0008750231
## 85 85 0.03217366 0.2190966 0.02506464 0.001410182 0.03086652 0.0008649159
## 86 86 0.03223055 0.2165903 0.02507377 0.001340014 0.02685902 0.0008620817
## 87 87 0.03225179 0.2154918 0.02508679 0.001327631 0.02635142 0.0008612842
## 88 88 0.03218326 0.2186594 0.02507630 0.001407589 0.03107952 0.0008724131
## 89 89 0.03223601 0.2162578 0.02509859 0.001323130 0.02672256 0.0008675088
## 90 90 0.03222869 0.2163234 0.02508410 0.001322355 0.02690422 0.0008443513
## 91 91 0.03222645 0.2162394 0.02508817 0.001322779 0.02768809 0.0008570497
## 92 92 0.03222131 0.2170589 0.02508740 0.001313760 0.02665403 0.0008446662
## 93 93 0.03222808 0.2167246 0.02509482 0.001325979 0.02800580 0.0008443620
## 94 94 0.03216404 0.2193865 0.02504202 0.001280143 0.02604697 0.0008198894
## 95 95 0.03220966 0.2177126 0.02506536 0.001306625 0.02617064 0.0008214433
## 96 96 0.03221366 0.2176087 0.02506833 0.001313508 0.02625488 0.0008252369
## 97 97 0.03224616 0.2156815 0.02508578 0.001284050 0.02462589 0.0008067351
## 98 98 0.03219379 0.2182939 0.02505424 0.001332201 0.02741835 0.0008270563
## 99 99 0.03222081 0.2166399 0.02506240 0.001265762 0.02499927 0.0008001542
## 100 100 0.03220873 0.2177996 0.02505367 0.001293550 0.02558046 0.0008145242
## 101 101 0.03218440 0.2191067 0.02502038 0.001294499 0.02709500 0.0008071130
## 102 102 0.03220142 0.2181472 0.02504322 0.001291011 0.02581538 0.0008207095
## 103 103 0.03219753 0.2183034 0.02504210 0.001281037 0.02570136 0.0008096457
## 104 104 0.03218424 0.2188754 0.02503180 0.001278422 0.02548358 0.0008085554
## 105 105 0.03215698 0.2199506 0.02501938 0.001312806 0.02711482 0.0008333186
## 106 106 0.03216494 0.2196126 0.02501188 0.001280391 0.02557929 0.0007991229
## 107 107 0.03216809 0.2196252 0.02501704 0.001272877 0.02545116 0.0007951466
## 108 108 0.03216808 0.2196173 0.02501264 0.001263216 0.02492189 0.0007931747
## 109 109 0.03220765 0.2175592 0.02503582 0.001228866 0.02507773 0.0007490572
## 110 110 0.03216281 0.2194696 0.02499774 0.001252452 0.02464754 0.0007822069
## 111 111 0.03217374 0.2194405 0.02500877 0.001265356 0.02477941 0.0007871575
## 112 112 0.03217897 0.2191993 0.02501609 0.001272554 0.02459325 0.0007988454
## 113 113 0.03221059 0.2175370 0.02505194 0.001231376 0.02489747 0.0007695118
## 114 114 0.03215465 0.2202602 0.02500504 0.001271621 0.02442841 0.0007996775
## 115 115 0.03215367 0.2203304 0.02500592 0.001272817 0.02438410 0.0007983731
## 116 116 0.03215443 0.2202206 0.02501805 0.001279327 0.02468808 0.0007913078
## 117 117 0.03215337 0.2203307 0.02500597 0.001289385 0.02477153 0.0008069133
## 118 118 0.03215319 0.2203658 0.02500312 0.001294660 0.02496730 0.0008111401
## 119 119 0.03214747 0.2206024 0.02500386 0.001295849 0.02485580 0.0008146161
## 120 120 0.03212725 0.2216414 0.02498119 0.001292636 0.02601157 0.0007946280
## 121 121 0.03214243 0.2208365 0.02500319 0.001292526 0.02479949 0.0008098072
## 122 122 0.03214673 0.2206589 0.02500628 0.001287106 0.02480052 0.0008030332
## 123 123 0.03214328 0.2207841 0.02499782 0.001289532 0.02489074 0.0008044744
## 124 124 0.03211689 0.2220490 0.02497051 0.001281663 0.02587525 0.0007909712
## 125 125 0.03213497 0.2211229 0.02499164 0.001282096 0.02472662 0.0008024946
## 126 126 0.03213254 0.2212350 0.02499147 0.001284816 0.02460441 0.0008020864
## 127 127 0.03213336 0.2208919 0.02498012 0.001288681 0.02546743 0.0008044800
## 128 128 0.03212743 0.2214716 0.02498858 0.001283676 0.02460828 0.0008032679
## 129 129 0.03213257 0.2212367 0.02499516 0.001283804 0.02476711 0.0008022912
## 130 130 0.03216825 0.2196590 0.02503435 0.001296565 0.02650897 0.0008314409
## 131 131 0.03214361 0.2207392 0.02500632 0.001281660 0.02448111 0.0007980568
## 132 132 0.03214713 0.2205711 0.02501125 0.001288916 0.02459372 0.0008063781
## 133 133 0.03214766 0.2205533 0.02500977 0.001291750 0.02465277 0.0008087701
## 134 134 0.03214943 0.2204043 0.02502909 0.001290122 0.02452057 0.0007947717
## 135 135 0.03216709 0.2195886 0.02502240 0.001269519 0.02461970 0.0007930243
## 136 136 0.03214999 0.2204607 0.02501303 0.001292264 0.02475503 0.0008076937
## 137 137 0.03215591 0.2200745 0.02501927 0.001290962 0.02591330 0.0008179877
## 138 138 0.03215248 0.2201059 0.02500481 0.001294733 0.02568932 0.0008105581
## 139 139 0.03215155 0.2204304 0.02501591 0.001295962 0.02521199 0.0008106315
## 140 140 0.03215958 0.2199987 0.02502902 0.001311941 0.02651818 0.0008377046
## 141 141 0.03215280 0.2203826 0.02501692 0.001293162 0.02523046 0.0008115562
## 142 142 0.03218000 0.2190930 0.02506015 0.001284810 0.02572728 0.0008080327
## 143 143 0.03218644 0.2187451 0.02507195 0.001291572 0.02571845 0.0008262860
## 144 144 0.03215505 0.2202574 0.02501788 0.001290488 0.02505785 0.0008160406
## 145 145 0.03217207 0.2194095 0.02504339 0.001272345 0.02451871 0.0007943683
## 146 146 0.03217032 0.2195361 0.02502441 0.001274138 0.02498885 0.0008059002
## 147 147 0.03220094 0.2180900 0.02506324 0.001263666 0.02363101 0.0007857309
## 148 148 0.03215565 0.2202454 0.02501659 0.001290369 0.02505835 0.0008146290
## 149 149 0.03216245 0.2198834 0.02502571 0.001303736 0.02546684 0.0008313923
## 150 150 0.03215597 0.2202318 0.02501680 0.001288054 0.02512420 0.0008109010
## 151 151 0.03215572 0.2202409 0.02501723 0.001287029 0.02506555 0.0008095030
## 152 152 0.03216535 0.2197636 0.02501903 0.001293670 0.02531494 0.0008113569
## 153 153 0.03216415 0.2198791 0.02501624 0.001274298 0.02521856 0.0007978609
## 154 154 0.03215900 0.2200496 0.02502126 0.001285577 0.02499426 0.0008100083
## 155 155 0.03215397 0.2203284 0.02501973 0.001277795 0.02568308 0.0007918531
## 156 156 0.03215651 0.2201276 0.02502549 0.001284651 0.02494687 0.0008004501
## 157 157 0.03217359 0.2193932 0.02503116 0.001294963 0.02560334 0.0008152898
## 158 158 0.03215957 0.2200378 0.02502870 0.001283079 0.02489780 0.0007995420
## 159 159 0.03216329 0.2198960 0.02503298 0.001281394 0.02483354 0.0007912617
## 160 160 0.03216528 0.2198199 0.02503462 0.001283491 0.02500424 0.0007916376
## 161 161 0.03215893 0.2200704 0.02502906 0.001284812 0.02496307 0.0007993303
## 162 162 0.03215962 0.2200953 0.02501711 0.001283095 0.02519516 0.0008018994
## 163 163 0.03215896 0.2200985 0.02501904 0.001284831 0.02506568 0.0008072135
## 164 164 0.03216074 0.2200205 0.02502151 0.001283672 0.02495766 0.0008069270
## [1] "Best Model"
## nvmax
## 124 124
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096659e+00 2.095830e+00 2.097487e+00
## PC1 -4.997658e-04 -5.723624e-04 -4.271691e-04
## PC2 -9.419626e-04 -1.015241e-03 -8.686837e-04
## PC3 -4.391224e-04 -5.136222e-04 -3.646225e-04
## PC4 -3.242618e-04 -3.994039e-04 -2.491197e-04
## PC5 1.765051e-04 9.986175e-05 2.531485e-04
## PC6 -9.231281e-05 -1.695287e-04 -1.509692e-05
## PC7 -2.082596e-04 -2.874469e-04 -1.290722e-04
## PC8 -4.693927e-05 -1.276475e-04 3.376897e-05
## PC9 -3.909225e-05 -1.212191e-04 4.303461e-05
## PC11 -5.810165e-04 -6.707886e-04 -4.912445e-04
## PC12 -4.676546e-04 -5.622673e-04 -3.730418e-04
## PC13 2.930867e-04 1.966760e-04 3.894975e-04
## PC14 2.344941e-04 1.347109e-04 3.342773e-04
## PC15 -3.911419e-05 -1.405327e-04 6.230431e-05
## PC16 3.058276e-04 2.032819e-04 4.083733e-04
## PC17 -1.701312e-04 -2.782192e-04 -6.204333e-05
## PC18 -3.519583e-04 -4.641377e-04 -2.397790e-04
## PC19 7.500380e-05 -3.907661e-05 1.890842e-04
## PC20 4.106839e-04 2.860206e-04 5.353471e-04
## PC21 1.003118e-04 -2.931462e-05 2.299383e-04
## PC23 2.287595e-04 -2.523984e-05 4.827588e-04
## PC24 -9.062350e-04 -1.199519e-03 -6.129510e-04
## PC25 1.862813e-04 -1.435207e-04 5.160832e-04
## PC26 4.823554e-04 1.469997e-04 8.177110e-04
## PC27 2.339783e-04 -1.089839e-04 5.769405e-04
## PC29 5.611705e-04 1.828666e-04 9.394743e-04
## PC31 -1.736812e-04 -5.854572e-04 2.380949e-04
## PC32 -7.551321e-04 -1.174630e-03 -3.356339e-04
## PC33 4.006520e-04 -2.659617e-05 8.279002e-04
## PC34 1.089153e-03 6.376159e-04 1.540691e-03
## PC37 -5.373194e-04 -1.042393e-03 -3.224590e-05
## PC38 2.849708e-04 -2.418253e-04 8.117669e-04
## PC39 -2.362448e-04 -7.775214e-04 3.050319e-04
## PC40 -2.997290e-04 -8.423369e-04 2.428789e-04
## PC41 -2.599751e-04 -8.170540e-04 2.971038e-04
## PC44 6.290816e-04 6.109832e-05 1.197065e-03
## PC46 1.968107e-04 -3.809470e-04 7.745684e-04
## PC47 -4.996877e-04 -1.076348e-03 7.697243e-05
## PC48 3.284368e-04 -2.479308e-04 9.048044e-04
## PC50 -2.767511e-04 -8.660549e-04 3.125526e-04
## PC51 2.887351e-04 -3.205127e-04 8.979829e-04
## PC54 -3.444124e-04 -9.535879e-04 2.647630e-04
## PC55 -2.019717e-04 -8.137421e-04 4.097987e-04
## PC59 9.408372e-04 3.177595e-04 1.563915e-03
## PC62 -4.323139e-04 -1.058433e-03 1.938047e-04
## PC63 -6.542496e-04 -1.285126e-03 -2.337289e-05
## PC64 -8.888503e-04 -1.525695e-03 -2.520054e-04
## PC66 -3.863940e-04 -1.027139e-03 2.543513e-04
## PC67 3.974831e-04 -2.465421e-04 1.041508e-03
## PC68 8.225872e-04 1.784373e-04 1.466737e-03
## PC69 4.439242e-04 -1.959698e-04 1.083818e-03
## PC71 3.673069e-04 -2.859701e-04 1.020584e-03
## PC73 3.476716e-04 -3.098426e-04 1.005186e-03
## PC74 -4.957264e-04 -1.156618e-03 1.651655e-04
## PC75 -8.646934e-04 -1.517344e-03 -2.120426e-04
## PC76 -2.949266e-04 -9.618776e-04 3.720243e-04
## PC77 3.958113e-04 -2.678934e-04 1.059516e-03
## PC79 6.774454e-04 -1.028822e-06 1.355920e-03
## PC80 -3.720502e-04 -1.048083e-03 3.039823e-04
## PC81 8.760508e-04 2.007494e-04 1.551352e-03
## PC82 2.760300e-04 -4.050903e-04 9.571503e-04
## PC83 -7.404018e-04 -1.422055e-03 -5.874850e-05
## PC84 5.688482e-04 -1.222141e-04 1.259910e-03
## PC85 1.132068e-03 4.430202e-04 1.821115e-03
## PC86 -3.199491e-04 -1.011677e-03 3.717785e-04
## PC87 1.856071e-03 1.165554e-03 2.546588e-03
## PC88 -9.436457e-04 -1.644344e-03 -2.429477e-04
## PC89 -7.220978e-04 -1.427100e-03 -1.709597e-05
## PC90 -9.642077e-04 -1.666900e-03 -2.615151e-04
## PC92 -3.067944e-04 -1.012283e-03 3.986939e-04
## PC93 3.952580e-04 -3.096411e-04 1.100157e-03
## PC94 -6.082842e-04 -1.319194e-03 1.026254e-04
## PC96 -4.615116e-04 -1.176606e-03 2.535832e-04
## PC97 -3.579184e-04 -1.074938e-03 3.591017e-04
## PC98 -5.814605e-04 -1.295714e-03 1.327928e-04
## PC99 -3.850739e-04 -1.103673e-03 3.335248e-04
## PC100 2.548386e-04 -4.622816e-04 9.719588e-04
## PC102 -7.647606e-04 -1.481113e-03 -4.840848e-05
## PC103 5.365540e-04 -1.825206e-04 1.255629e-03
## PC104 -9.099239e-04 -1.630139e-03 -1.897084e-04
## PC105 9.468319e-04 2.250600e-04 1.668604e-03
## PC106 7.199742e-04 -6.395549e-06 1.446344e-03
## PC108 2.510471e-04 -4.739897e-04 9.760839e-04
## PC110 -5.150037e-04 -1.244192e-03 2.141848e-04
## PC111 -5.564896e-04 -1.283900e-03 1.709204e-04
## PC113 2.520449e-04 -4.808782e-04 9.849680e-04
## PC114 -6.700358e-04 -1.399527e-03 5.945587e-05
## PC115 -1.569273e-03 -2.310368e-03 -8.281787e-04
## PC118 3.622080e-04 -3.767847e-04 1.101201e-03
## PC119 -8.696544e-04 -1.611315e-03 -1.279942e-04
## PC120 3.561252e-04 -3.830543e-04 1.095305e-03
## PC121 -4.511182e-04 -1.195585e-03 2.933490e-04
## PC122 6.495029e-04 -9.519583e-05 1.394202e-03
## PC123 -6.912184e-04 -1.433141e-03 5.070373e-05
## PC124 4.813707e-04 -2.622837e-04 1.225025e-03
## PC125 4.965890e-04 -2.554384e-04 1.248616e-03
## PC127 6.695609e-04 -7.681537e-05 1.415937e-03
## PC128 -9.699995e-04 -1.719401e-03 -2.205976e-04
## PC131 -1.138864e-03 -1.894067e-03 -3.836605e-04
## PC132 2.479453e-04 -5.033553e-04 9.992459e-04
## PC134 7.156726e-04 -3.984502e-05 1.471190e-03
## PC135 4.064518e-04 -3.519045e-04 1.164808e-03
## PC136 5.759509e-04 -1.752275e-04 1.327129e-03
## PC137 -2.976947e-04 -1.051023e-03 4.556341e-04
## PC138 3.849774e-04 -3.729822e-04 1.142937e-03
## PC139 -9.271984e-04 -1.687508e-03 -1.668891e-04
## PC140 -4.131939e-04 -1.177735e-03 3.513470e-04
## PC143 3.846308e-04 -3.807100e-04 1.149972e-03
## PC144 7.586957e-04 -4.079424e-06 1.521471e-03
## PC145 3.843754e-04 -3.818809e-04 1.150632e-03
## PC146 7.268206e-04 -4.075834e-05 1.494400e-03
## PC147 -2.733259e-04 -1.046434e-03 4.997820e-04
## PC148 -5.575318e-04 -1.329454e-03 2.143908e-04
## PC150 4.804003e-04 -2.898563e-04 1.250657e-03
## PC151 5.801210e-04 -1.949755e-04 1.355217e-03
## PC152 -5.376380e-04 -1.305558e-03 2.302819e-04
## PC153 8.797658e-04 1.081048e-04 1.651427e-03
## PC154 -1.031704e-03 -1.801461e-03 -2.619474e-04
## PC155 9.919059e-04 2.172260e-04 1.766586e-03
## PC156 5.465264e-04 -2.348923e-04 1.327945e-03
## PC159 1.541973e-03 7.709181e-04 2.313028e-03
## PC162 -1.399424e-03 -2.177076e-03 -6.217719e-04
## PC163 6.740592e-04 -1.103491e-04 1.458468e-03
## PC164 4.061922e-04 -3.823332e-04 1.194718e-03Test
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.011 2.088 2.100 2.097 2.110 2.135
## [1] "leapSeq Test MSE: 0.000991647321730291"
## [1] "leapSeq Test RMSE: 0.031490432225206"
## [1] "leapSeq Test MSE (Org Scale): 89.371209069609"
## [1] "leapSeq Test RMSE (Org Scale): 9.45363470151079"
LASSO with CV
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.000231 on full training set
## glmnet
##
## 5584 samples
## 164 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.03206691 0.22273155 0.02495043
## 0.0001047616 0.03206391 0.22282063 0.02494799
## 0.0001097499 0.03206091 0.22291004 0.02494550
## 0.0001149757 0.03205796 0.22299671 0.02494305
## 0.0001204504 0.03205507 0.22308091 0.02494064
## 0.0001261857 0.03205221 0.22316453 0.02493836
## 0.0001321941 0.03204941 0.22324608 0.02493617
## 0.0001384886 0.03204672 0.22332370 0.02493407
## 0.0001450829 0.03204420 0.22339517 0.02493216
## 0.0001519911 0.03204171 0.22346690 0.02493028
## 0.0001592283 0.03203933 0.22353503 0.02492844
## 0.0001668101 0.03203700 0.22360310 0.02492666
## 0.0001747528 0.03203481 0.22366723 0.02492496
## 0.0001830738 0.03203288 0.22372216 0.02492329
## 0.0001917910 0.03203121 0.22376933 0.02492182
## 0.0002009233 0.03202984 0.22380592 0.02492066
## 0.0002104904 0.03202876 0.22383321 0.02491968
## 0.0002205131 0.03202816 0.22384278 0.02491900
## 0.0002310130 0.03202780 0.22384676 0.02491856
## 0.0002420128 0.03202791 0.22383505 0.02491848
## 0.0002535364 0.03202843 0.22381065 0.02491862
## 0.0002656088 0.03202946 0.22376909 0.02491928
## 0.0002782559 0.03203110 0.22370545 0.02492053
## 0.0002915053 0.03203306 0.22363569 0.02492237
## 0.0003053856 0.03203559 0.22354857 0.02492491
## 0.0003199267 0.03203878 0.22344109 0.02492788
## 0.0003351603 0.03204264 0.22331225 0.02493144
## 0.0003511192 0.03204682 0.22318108 0.02493503
## 0.0003678380 0.03205092 0.22306905 0.02493802
## 0.0003853529 0.03205564 0.22294090 0.02494093
## 0.0004037017 0.03206097 0.22279969 0.02494367
## 0.0004229243 0.03206731 0.22262537 0.02494775
## 0.0004430621 0.03207470 0.22241689 0.02495259
## 0.0004641589 0.03208274 0.22219555 0.02495802
## 0.0004862602 0.03209152 0.22195794 0.02496417
## 0.0005094138 0.03210119 0.22169865 0.02497092
## 0.0005336699 0.03211197 0.22140865 0.02497811
## 0.0005590810 0.03212387 0.22108573 0.02498648
## 0.0005857021 0.03213675 0.22073930 0.02499542
## 0.0006135907 0.03215144 0.22032263 0.02500538
## 0.0006428073 0.03216723 0.21987524 0.02501579
## 0.0006734151 0.03218542 0.21932544 0.02502758
## 0.0007054802 0.03220531 0.21871222 0.02504081
## 0.0007390722 0.03222726 0.21801751 0.02505641
## 0.0007742637 0.03225082 0.21726814 0.02507334
## 0.0008111308 0.03227619 0.21645139 0.02509152
## 0.0008497534 0.03230376 0.21554615 0.02511139
## 0.0008902151 0.03233253 0.21460422 0.02513263
## 0.0009326033 0.03236245 0.21363124 0.02515506
## 0.0009770100 0.03239437 0.21257490 0.02517818
## 0.0010235310 0.03242824 0.21144012 0.02520305
## 0.0010722672 0.03246467 0.21019135 0.02523016
## 0.0011233240 0.03250367 0.20882714 0.02525922
## 0.0011768120 0.03254472 0.20737691 0.02528891
## 0.0012328467 0.03258719 0.20587836 0.02531991
## 0.0012915497 0.03263218 0.20425443 0.02535444
## 0.0013530478 0.03268071 0.20245385 0.02539259
## 0.0014174742 0.03273113 0.20058074 0.02543315
## 0.0014849683 0.03278394 0.19861023 0.02547449
## 0.0015556761 0.03283961 0.19651017 0.02551767
## 0.0016297508 0.03289780 0.19429990 0.02556230
## 0.0017073526 0.03296067 0.19182999 0.02560999
## 0.0017886495 0.03302663 0.18919372 0.02565996
## 0.0018738174 0.03309465 0.18645303 0.02571082
## 0.0019630407 0.03316465 0.18360519 0.02576381
## 0.0020565123 0.03323661 0.18064880 0.02581820
## 0.0021544347 0.03331106 0.17754247 0.02587536
## 0.0022570197 0.03338658 0.17439772 0.02593247
## 0.0023644894 0.03346288 0.17122249 0.02598912
## 0.0024770764 0.03353856 0.16811213 0.02604487
## 0.0025950242 0.03361084 0.16525317 0.02609812
## 0.0027185882 0.03368216 0.16253185 0.02615112
## 0.0028480359 0.03375246 0.15996791 0.02620376
## 0.0029836472 0.03382541 0.15730335 0.02625793
## 0.0031257158 0.03390285 0.15437395 0.02631551
## 0.0032745492 0.03398526 0.15108974 0.02637643
## 0.0034304693 0.03407237 0.14743846 0.02644037
## 0.0035938137 0.03416165 0.14364904 0.02650688
## 0.0037649358 0.03425401 0.13960415 0.02657682
## 0.0039442061 0.03435186 0.13505242 0.02664947
## 0.0041320124 0.03445355 0.13006914 0.02672408
## 0.0043287613 0.03455652 0.12489601 0.02679935
## 0.0045348785 0.03466265 0.11929005 0.02687605
## 0.0047508102 0.03477428 0.11293742 0.02695476
## 0.0049770236 0.03489122 0.10573843 0.02703583
## 0.0052140083 0.03499735 0.09942032 0.02710982
## 0.0054622772 0.03509164 0.09407642 0.02717650
## 0.0057223677 0.03517014 0.09042241 0.02723150
## 0.0059948425 0.03523158 0.08865713 0.02727428
## 0.0062802914 0.03528952 0.08765748 0.02731403
## 0.0065793322 0.03534464 0.08753580 0.02735176
## 0.0068926121 0.03540425 0.08753580 0.02739312
## 0.0072208090 0.03546956 0.08753580 0.02743846
## 0.0075646333 0.03554109 0.08753580 0.02748881
## 0.0079248290 0.03561944 0.08753580 0.02754457
## 0.0083021757 0.03570523 0.08753580 0.02760591
## 0.0086974900 0.03579916 0.08753580 0.02767336
## 0.0091116276 0.03590195 0.08753580 0.02774740
## 0.0095454846 0.03601444 0.08753580 0.02782846
## 0.0100000000 0.03613749 0.08753580 0.02791698
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.000231013.
## alpha lambda
## 19 1 0.000231013
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.03206691 0.22273155 0.02495043 0.001301184 0.02629425 0.0008268577
## 2 1 0.0001047616 0.03206391 0.22282063 0.02494799 0.001301748 0.02636188 0.0008275958
## 3 1 0.0001097499 0.03206091 0.22291004 0.02494550 0.001302386 0.02643705 0.0008284132
## 4 1 0.0001149757 0.03205796 0.22299671 0.02494305 0.001303004 0.02651346 0.0008292026
## 5 1 0.0001204504 0.03205507 0.22308091 0.02494064 0.001303614 0.02659290 0.0008300075
## 6 1 0.0001261857 0.03205221 0.22316453 0.02493836 0.001304230 0.02667516 0.0008309140
## 7 1 0.0001321941 0.03204941 0.22324608 0.02493617 0.001304883 0.02676276 0.0008319103
## 8 1 0.0001384886 0.03204672 0.22332370 0.02493407 0.001305724 0.02686022 0.0008329435
## 9 1 0.0001450829 0.03204420 0.22339517 0.02493216 0.001306668 0.02697188 0.0008341111
## 10 1 0.0001519911 0.03204171 0.22346690 0.02493028 0.001307587 0.02709014 0.0008352419
## 11 1 0.0001592283 0.03203933 0.22353503 0.02492844 0.001308563 0.02721720 0.0008364414
## 12 1 0.0001668101 0.03203700 0.22360310 0.02492666 0.001309445 0.02734968 0.0008376470
## 13 1 0.0001747528 0.03203481 0.22366723 0.02492496 0.001310361 0.02749060 0.0008389737
## 14 1 0.0001830738 0.03203288 0.22372216 0.02492329 0.001311381 0.02764172 0.0008404477
## 15 1 0.0001917910 0.03203121 0.22376933 0.02492182 0.001312463 0.02780157 0.0008421437
## 16 1 0.0002009233 0.03202984 0.22380592 0.02492066 0.001313664 0.02796884 0.0008440928
## 17 1 0.0002104904 0.03202876 0.22383321 0.02491968 0.001314828 0.02813608 0.0008460493
## 18 1 0.0002205131 0.03202816 0.22384278 0.02491900 0.001316252 0.02831730 0.0008480620
## 19 1 0.0002310130 0.03202780 0.22384676 0.02491856 0.001317648 0.02850711 0.0008502188
## 20 1 0.0002420128 0.03202791 0.22383505 0.02491848 0.001319224 0.02871348 0.0008524270
## 21 1 0.0002535364 0.03202843 0.22381065 0.02491862 0.001320917 0.02893552 0.0008548890
## 22 1 0.0002656088 0.03202946 0.22376909 0.02491928 0.001322487 0.02915692 0.0008572801
## 23 1 0.0002782559 0.03203110 0.22370545 0.02492053 0.001324068 0.02938239 0.0008596569
## 24 1 0.0002915053 0.03203306 0.22363569 0.02492237 0.001325542 0.02961107 0.0008621045
## 25 1 0.0003053856 0.03203559 0.22354857 0.02492491 0.001327144 0.02985294 0.0008644832
## 26 1 0.0003199267 0.03203878 0.22344109 0.02492788 0.001328868 0.03010651 0.0008668954
## 27 1 0.0003351603 0.03204264 0.22331225 0.02493144 0.001330713 0.03037107 0.0008690598
## 28 1 0.0003511192 0.03204682 0.22318108 0.02493503 0.001332808 0.03062660 0.0008713043
## 29 1 0.0003678380 0.03205092 0.22306905 0.02493802 0.001334635 0.03086721 0.0008730631
## 30 1 0.0003853529 0.03205564 0.22294090 0.02494093 0.001335948 0.03110943 0.0008746998
## 31 1 0.0004037017 0.03206097 0.22279969 0.02494367 0.001336935 0.03134211 0.0008756920
## 32 1 0.0004229243 0.03206731 0.22262537 0.02494775 0.001337175 0.03157925 0.0008760306
## 33 1 0.0004430621 0.03207470 0.22241689 0.02495259 0.001337013 0.03182420 0.0008762115
## 34 1 0.0004641589 0.03208274 0.22219555 0.02495802 0.001336551 0.03210970 0.0008765049
## 35 1 0.0004862602 0.03209152 0.22195794 0.02496417 0.001336165 0.03243373 0.0008765803
## 36 1 0.0005094138 0.03210119 0.22169865 0.02497092 0.001335336 0.03278721 0.0008761730
## 37 1 0.0005336699 0.03211197 0.22140865 0.02497811 0.001334457 0.03317385 0.0008755025
## 38 1 0.0005590810 0.03212387 0.22108573 0.02498648 0.001333403 0.03356634 0.0008750911
## 39 1 0.0005857021 0.03213675 0.22073930 0.02499542 0.001332357 0.03396576 0.0008739453
## 40 1 0.0006135907 0.03215144 0.22032263 0.02500538 0.001330777 0.03432230 0.0008725561
## 41 1 0.0006428073 0.03216723 0.21987524 0.02501579 0.001328523 0.03461141 0.0008706940
## 42 1 0.0006734151 0.03218542 0.21932544 0.02502758 0.001326330 0.03486695 0.0008692381
## 43 1 0.0007054802 0.03220531 0.21871222 0.02504081 0.001323669 0.03508322 0.0008681489
## 44 1 0.0007390722 0.03222726 0.21801751 0.02505641 0.001320641 0.03524005 0.0008662818
## 45 1 0.0007742637 0.03225082 0.21726814 0.02507334 0.001316838 0.03533547 0.0008628490
## 46 1 0.0008111308 0.03227619 0.21645139 0.02509152 0.001312329 0.03539944 0.0008579621
## 47 1 0.0008497534 0.03230376 0.21554615 0.02511139 0.001307851 0.03545621 0.0008525260
## 48 1 0.0008902151 0.03233253 0.21460422 0.02513263 0.001303854 0.03555253 0.0008482212
## 49 1 0.0009326033 0.03236245 0.21363124 0.02515506 0.001299750 0.03565113 0.0008436369
## 50 1 0.0009770100 0.03239437 0.21257490 0.02517818 0.001295936 0.03569740 0.0008391248
## 51 1 0.0010235310 0.03242824 0.21144012 0.02520305 0.001292076 0.03567792 0.0008352084
## 52 1 0.0010722672 0.03246467 0.21019135 0.02523016 0.001287740 0.03565971 0.0008313204
## 53 1 0.0011233240 0.03250367 0.20882714 0.02525922 0.001283214 0.03562620 0.0008267793
## 54 1 0.0011768120 0.03254472 0.20737691 0.02528891 0.001279594 0.03560564 0.0008228628
## 55 1 0.0012328467 0.03258719 0.20587836 0.02531991 0.001276106 0.03555858 0.0008189733
## 56 1 0.0012915497 0.03263218 0.20425443 0.02535444 0.001270932 0.03546545 0.0008145193
## 57 1 0.0013530478 0.03268071 0.20245385 0.02539259 0.001265262 0.03533846 0.0008089808
## 58 1 0.0014174742 0.03273113 0.20058074 0.02543315 0.001259478 0.03525494 0.0008049380
## 59 1 0.0014849683 0.03278394 0.19861023 0.02547449 0.001254152 0.03516183 0.0008008046
## 60 1 0.0015556761 0.03283961 0.19651017 0.02551767 0.001249845 0.03509915 0.0007974267
## 61 1 0.0016297508 0.03289780 0.19429990 0.02556230 0.001246188 0.03498435 0.0007938842
## 62 1 0.0017073526 0.03296067 0.19182999 0.02560999 0.001243260 0.03485858 0.0007909743
## 63 1 0.0017886495 0.03302663 0.18919372 0.02565996 0.001239240 0.03458251 0.0007866890
## 64 1 0.0018738174 0.03309465 0.18645303 0.02571082 0.001233825 0.03431504 0.0007820097
## 65 1 0.0019630407 0.03316465 0.18360519 0.02576381 0.001227575 0.03392991 0.0007770585
## 66 1 0.0020565123 0.03323661 0.18064880 0.02581820 0.001220223 0.03360988 0.0007720950
## 67 1 0.0021544347 0.03331106 0.17754247 0.02587536 0.001212511 0.03317658 0.0007660547
## 68 1 0.0022570197 0.03338658 0.17439772 0.02593247 0.001205411 0.03290893 0.0007606235
## 69 1 0.0023644894 0.03346288 0.17122249 0.02598912 0.001198541 0.03254935 0.0007544805
## 70 1 0.0024770764 0.03353856 0.16811213 0.02604487 0.001193000 0.03221190 0.0007480254
## 71 1 0.0025950242 0.03361084 0.16525317 0.02609812 0.001186845 0.03133578 0.0007387651
## 72 1 0.0027185882 0.03368216 0.16253185 0.02615112 0.001181758 0.03059021 0.0007315860
## 73 1 0.0028480359 0.03375246 0.15996791 0.02620376 0.001176745 0.02972760 0.0007245296
## 74 1 0.0029836472 0.03382541 0.15730335 0.02625793 0.001170248 0.02896053 0.0007167329
## 75 1 0.0031257158 0.03390285 0.15437395 0.02631551 0.001164510 0.02816716 0.0007098716
## 76 1 0.0032745492 0.03398526 0.15108974 0.02637643 0.001158704 0.02730925 0.0007031831
## 77 1 0.0034304693 0.03407237 0.14743846 0.02644037 0.001151462 0.02625801 0.0006957113
## 78 1 0.0035938137 0.03416165 0.14364904 0.02650688 0.001143052 0.02539118 0.0006869717
## 79 1 0.0037649358 0.03425401 0.13960415 0.02657682 0.001135647 0.02435175 0.0006767473
## 80 1 0.0039442061 0.03435186 0.13505242 0.02664947 0.001129496 0.02336392 0.0006675005
## 81 1 0.0041320124 0.03445355 0.13006914 0.02672408 0.001121707 0.02214163 0.0006589907
## 82 1 0.0043287613 0.03455652 0.12489601 0.02679935 0.001114111 0.02129832 0.0006495905
## 83 1 0.0045348785 0.03466265 0.11929005 0.02687605 0.001108719 0.02039996 0.0006404807
## 84 1 0.0047508102 0.03477428 0.11293742 0.02695476 0.001105383 0.01972434 0.0006334689
## 85 1 0.0049770236 0.03489122 0.10573843 0.02703583 0.001102942 0.01895416 0.0006272675
## 86 1 0.0052140083 0.03499735 0.09942032 0.02710982 0.001103551 0.01915754 0.0006230842
## 87 1 0.0054622772 0.03509164 0.09407642 0.02717650 0.001106203 0.01873843 0.0006208467
## 88 1 0.0057223677 0.03517014 0.09042241 0.02723150 0.001105430 0.01942431 0.0006173868
## 89 1 0.0059948425 0.03523158 0.08865713 0.02727428 0.001103603 0.01882196 0.0006131887
## 90 1 0.0062802914 0.03528952 0.08765748 0.02731403 0.001104265 0.01873406 0.0006114533
## 91 1 0.0065793322 0.03534464 0.08753580 0.02735176 0.001108800 0.01850564 0.0006119928
## 92 1 0.0068926121 0.03540425 0.08753580 0.02739312 0.001111828 0.01850564 0.0006104488
## 93 1 0.0072208090 0.03546956 0.08753580 0.02743846 0.001115087 0.01850564 0.0006090071
## 94 1 0.0075646333 0.03554109 0.08753580 0.02748881 0.001118598 0.01850564 0.0006084258
## 95 1 0.0079248290 0.03561944 0.08753580 0.02754457 0.001122384 0.01850564 0.0006088559
## 96 1 0.0083021757 0.03570523 0.08753580 0.02760591 0.001126470 0.01850564 0.0006088667
## 97 1 0.0086974900 0.03579916 0.08753580 0.02767336 0.001130884 0.01850564 0.0006102204
## 98 1 0.0091116276 0.03590195 0.08753580 0.02774740 0.001135658 0.01850564 0.0006110478
## 99 1 0.0095454846 0.03601444 0.08753580 0.02782846 0.001140824 0.01850564 0.0006113757
## 100 1 0.0100000000 0.03613749 0.08753580 0.02791698 0.001146421 0.01850564 0.0006121823
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 2.096658e+00
## PC1 -4.799507e-04
## PC2 -9.202807e-04
## PC3 -4.188304e-04
## PC4 -3.036556e-04
## PC5 1.545492e-04
## PC6 -7.287966e-05
## PC7 -1.852841e-04
## PC8 -2.371220e-05
## PC9 -1.473350e-05
## PC11 -5.574330e-04
## PC12 -4.432590e-04
## PC13 2.658715e-04
## PC14 2.057163e-04
## PC15 -9.883151e-06
## PC16 2.820791e-04
## PC17 -1.397320e-04
## PC18 -3.223685e-04
## PC19 4.371053e-05
## PC20 3.759103e-04
## PC21 6.562980e-05
## PC23 1.604885e-04
## PC24 -8.127199e-04
## PC25 9.447366e-05
## PC26 3.883762e-04
## PC27 1.433760e-04
## PC29 4.678172e-04
## PC31 -5.083275e-05
## PC32 -6.229101e-04
## PC33 2.752230e-04
## PC34 9.643209e-04
## PC37 -3.961231e-04
## PC38 1.317506e-04
## PC39 -9.073278e-05
## PC40 -1.419130e-04
## PC41 -9.691812e-05
## PC44 4.563543e-04
## PC46 2.482365e-05
## PC47 -3.559654e-04
## PC48 1.462162e-04
## PC49 3.190472e-05
## PC50 -1.005604e-04
## PC51 9.709880e-05
## PC52 4.559111e-05
## PC53 1.685521e-05
## PC54 -1.418605e-04
## PC55 -3.777624e-06
## PC59 7.663104e-04
## PC62 -2.485663e-04
## PC63 -4.533437e-04
## PC64 -6.967440e-04
## PC66 -2.249583e-04
## PC67 2.018743e-04
## PC68 6.493853e-04
## PC69 2.705157e-04
## PC71 1.870183e-04
## PC73 1.520674e-04
## PC74 -3.101111e-04
## PC75 -6.621970e-04
## PC76 -9.430839e-05
## PC77 2.122278e-04
## PC78 2.856317e-06
## PC79 4.491448e-04
## PC80 -2.072996e-04
## PC81 6.794533e-04
## PC82 7.453161e-05
## PC83 -5.500302e-04
## PC84 3.827331e-04
## PC85 9.556405e-04
## PC86 -1.472490e-04
## PC87 1.686909e-03
## PC88 -7.844941e-04
## PC89 -5.265443e-04
## PC90 -7.423377e-04
## PC92 -9.137152e-05
## PC93 1.950928e-04
## PC94 -3.926244e-04
## PC96 -2.532271e-04
## PC97 -1.626748e-04
## PC98 -3.879666e-04
## PC99 -1.842468e-04
## PC100 4.332014e-05
## PC102 -5.730935e-04
## PC103 3.211222e-04
## PC104 -7.007930e-04
## PC105 7.593030e-04
## PC106 5.196788e-04
## PC107 1.849664e-06
## PC108 3.840142e-05
## PC110 -3.029180e-04
## PC111 -3.680055e-04
## PC113 9.948791e-06
## PC114 -4.921065e-04
## PC115 -1.352155e-03
## PC118 1.366918e-04
## PC119 -6.466373e-04
## PC120 1.570469e-04
## PC121 -2.330221e-04
## PC122 4.255873e-04
## PC123 -5.002018e-04
## PC124 2.656131e-04
## PC125 3.067373e-04
## PC127 4.568164e-04
## PC128 -7.472134e-04
## PC130 3.661383e-05
## PC131 -9.552720e-04
## PC132 4.168643e-05
## PC134 4.966364e-04
## PC135 1.731627e-04
## PC136 3.573157e-04
## PC137 -6.419016e-05
## PC138 1.527863e-04
## PC139 -6.879850e-04
## PC140 -2.205019e-04
## PC143 1.841870e-04
## PC144 5.571087e-04
## PC145 1.711036e-04
## PC146 5.228375e-04
## PC147 -2.538072e-05
## PC148 -3.229516e-04
## PC150 2.512381e-04
## PC151 3.735442e-04
## PC152 -3.215586e-04
## PC153 6.591491e-04
## PC154 -8.289342e-04
## PC155 7.768053e-04
## PC156 3.520305e-04
## PC159 1.306405e-03
## PC160 -4.432069e-06
## PC162 -1.180210e-03
## PC163 4.714407e-04
## PC164 1.654573e-04Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.020 2.089 2.100 2.097 2.108 2.131
## [1] "glmnet LASSO Test MSE: 0.000979874292188973"
## [1] "glmnet LASSO Test RMSE: 0.0313029438262438"
## [1] "glmnet LASSO Test MSE (Org Scale): 88.393945839481"
## [1] "glmnet LASSO Test RMSE (Org Scale): 9.40180545637278"
LARS with CV
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.758 on full training set
## Least Angle Regression
##
## 5584 samples
## 164 predictor
##
## Pre-processing: centered (164), scaled (164)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.03633304 NaN 0.02805647
## 0.01010101 0.03594473 0.08753580 0.02777660
## 0.02020202 0.03560752 0.08753580 0.02753502
## 0.03030303 0.03532291 0.08753813 0.02733629
## 0.04040404 0.03510328 0.09327323 0.02718199
## 0.05050505 0.03489864 0.10534976 0.02703808
## 0.06060606 0.03470472 0.11726401 0.02690229
## 0.07070707 0.03452341 0.12673322 0.02677245
## 0.08080808 0.03435738 0.13505587 0.02665108
## 0.09090909 0.03420002 0.14229513 0.02653332
## 0.10101010 0.03405726 0.14826356 0.02642617
## 0.11111111 0.03392161 0.15385061 0.02632679
## 0.12121212 0.03379411 0.15863145 0.02623270
## 0.13131313 0.03368381 0.16259280 0.02615037
## 0.14141414 0.03358645 0.16629656 0.02607975
## 0.15151515 0.03349410 0.16991903 0.02601197
## 0.16161616 0.03340519 0.17358212 0.02594618
## 0.17171717 0.03331591 0.17736025 0.02587875
## 0.18181818 0.03323082 0.18094079 0.02581407
## 0.19191919 0.03315114 0.18422514 0.02575318
## 0.20202020 0.03307613 0.18723946 0.02569655
## 0.21212121 0.03300423 0.19013139 0.02564268
## 0.22222222 0.03293600 0.19283179 0.02559089
## 0.23232323 0.03287153 0.19532237 0.02554160
## 0.24242424 0.03281121 0.19758730 0.02549441
## 0.25252525 0.03275397 0.19971506 0.02544903
## 0.26262626 0.03270103 0.20169065 0.02540642
## 0.27272727 0.03265212 0.20350437 0.02536807
## 0.28282828 0.03260754 0.20512489 0.02533427
## 0.29292929 0.03256683 0.20656808 0.02530395
## 0.30303030 0.03253043 0.20782590 0.02527742
## 0.31313131 0.03249573 0.20903467 0.02525172
## 0.32323232 0.03246350 0.21014862 0.02522821
## 0.33333333 0.03243296 0.21120360 0.02520585
## 0.34343434 0.03240473 0.21215413 0.02518466
## 0.35353535 0.03237881 0.21300860 0.02516534
## 0.36363636 0.03235510 0.21376891 0.02514773
## 0.37373737 0.03233246 0.21450822 0.02513077
## 0.38383838 0.03230980 0.21527687 0.02511413
## 0.39393939 0.03228875 0.21597715 0.02509883
## 0.40404040 0.03226976 0.21658862 0.02508529
## 0.41414141 0.03225217 0.21714198 0.02507293
## 0.42424242 0.03223510 0.21768955 0.02506081
## 0.43434343 0.03221920 0.21819476 0.02505001
## 0.44444444 0.03220441 0.21866153 0.02503992
## 0.45454545 0.03219072 0.21907952 0.02503050
## 0.46464646 0.03217769 0.21947493 0.02502175
## 0.47474747 0.03216548 0.21983918 0.02501350
## 0.48484848 0.03215402 0.22017821 0.02500597
## 0.49494949 0.03214360 0.22047675 0.02499900
## 0.50505051 0.03213402 0.22074372 0.02499248
## 0.51515152 0.03212522 0.22097889 0.02498662
## 0.52525253 0.03211655 0.22121862 0.02498089
## 0.53535354 0.03210843 0.22144371 0.02497555
## 0.54545455 0.03210123 0.22163516 0.02497072
## 0.55555556 0.03209450 0.22181533 0.02496616
## 0.56565657 0.03208819 0.22198360 0.02496166
## 0.57575758 0.03208202 0.22215620 0.02495731
## 0.58585859 0.03207606 0.22232689 0.02495324
## 0.59595960 0.03207043 0.22248950 0.02494952
## 0.60606061 0.03206507 0.22264797 0.02494593
## 0.61616162 0.03206034 0.22278358 0.02494309
## 0.62626263 0.03205640 0.22288952 0.02494105
## 0.63636364 0.03205281 0.22298714 0.02493898
## 0.64646465 0.03204961 0.22307404 0.02493681
## 0.65656566 0.03204642 0.22316937 0.02493416
## 0.66666667 0.03204309 0.22327910 0.02493131
## 0.67676768 0.03203971 0.22339752 0.02492833
## 0.68686869 0.03203696 0.22349168 0.02492575
## 0.69696970 0.03203467 0.22357032 0.02492349
## 0.70707071 0.03203261 0.22364505 0.02492163
## 0.71717172 0.03203065 0.22372206 0.02491995
## 0.72727273 0.03202937 0.22377170 0.02491899
## 0.73737374 0.03202859 0.22380316 0.02491863
## 0.74747475 0.03202807 0.22382793 0.02491860
## 0.75757576 0.03202800 0.22383937 0.02491879
## 0.76767677 0.03202821 0.22384436 0.02491923
## 0.77777778 0.03202897 0.22382999 0.02491997
## 0.78787879 0.03203025 0.22379842 0.02492103
## 0.79797980 0.03203201 0.22375022 0.02492263
## 0.80808081 0.03203433 0.22368313 0.02492461
## 0.81818182 0.03203711 0.22360268 0.02492686
## 0.82828283 0.03204024 0.22351281 0.02492927
## 0.83838384 0.03204366 0.22341542 0.02493189
## 0.84848485 0.03204747 0.22330785 0.02493483
## 0.85858586 0.03205187 0.22318104 0.02493825
## 0.86868687 0.03205681 0.22303697 0.02494224
## 0.87878788 0.03206223 0.22287746 0.02494673
## 0.88888889 0.03206830 0.22269606 0.02495166
## 0.89898990 0.03207460 0.22251145 0.02495672
## 0.90909091 0.03208134 0.22231410 0.02496229
## 0.91919192 0.03208857 0.22210179 0.02496797
## 0.92929293 0.03209631 0.22187439 0.02497387
## 0.93939394 0.03210468 0.22162633 0.02498010
## 0.94949495 0.03211309 0.22138215 0.02498636
## 0.95959596 0.03212168 0.22113625 0.02499285
## 0.96969697 0.03213062 0.22088171 0.02499956
## 0.97979798 0.03214005 0.22061426 0.02500645
## 0.98989899 0.03215022 0.22032139 0.02501379
## 1.00000000 0.03216074 0.22002046 0.02502151
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.7575758.
## fraction
## 76 0.7575758## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## -5.485657e-03 -1.041466e-02 -4.666547e-03 -3.352334e-03 1.674324e-03 -7.843493e-04 -1.941968e-03 -2.456482e-04
## PC9 PC11 PC12 PC13 PC14 PC15 PC16 PC17
## -1.508113e-04 -5.148967e-03 -3.885866e-03 2.289433e-03 1.710877e-03 -8.274828e-05 2.281916e-03 -1.073565e-03
## PC18 PC19 PC20 PC21 PC23 PC24 PC25 PC26
## -2.383663e-03 3.195022e-04 2.501730e-03 4.212262e-04 5.264985e-04 -2.299298e-03 2.392920e-04 9.617553e-04
## PC27 PC29 PC31 PC32 PC33 PC34 PC37 PC38
## 3.486263e-04 1.026691e-03 -1.043353e-04 -1.233282e-03 5.358367e-04 1.772480e-03 -6.520341e-04 2.093846e-04
## PC39 PC40 PC41 PC44 PC46 PC47 PC48 PC49
## -1.409753e-04 -2.188864e-04 -1.465466e-04 6.691759e-04 3.759333e-05 -5.136293e-04 2.124405e-04 4.668183e-05
## PC50 PC51 PC52 PC53 PC54 PC55 PC59 PC62
## -1.434519e-04 1.343929e-04 6.471637e-05 2.515771e-05 -1.954908e-04 -4.805508e-06 1.022173e-03 -3.312307e-04
## PC63 PC64 PC66 PC67 PC68 PC69 PC71 PC73
## -5.981931e-04 -9.097403e-04 -2.928747e-04 2.619159e-04 8.380380e-04 3.522387e-04 2.392924e-04 1.936656e-04
## PC74 PC75 PC76 PC77 PC79 PC80 PC81 PC82
## -3.908251e-04 -8.434583e-04 -1.192546e-04 2.671789e-04 5.511900e-04 -2.558768e-04 8.357282e-04 9.270868e-05
## PC83 PC84 PC85 PC86 PC87 PC88 PC89 PC90
## -6.710509e-04 4.609955e-04 1.151090e-03 -1.781077e-04 2.026792e-03 -9.300281e-04 -6.212049e-04 -8.781471e-04
## PC92 PC93 PC94 PC96 PC97 PC98 PC99 PC100
## -1.094686e-04 2.312894e-04 -4.600767e-04 -2.954271e-04 -1.898988e-04 -4.524109e-04 -2.143553e-04 5.203105e-05
## PC102 PC103 PC104 PC105 PC106 PC108 PC110 PC111
## -6.647983e-04 3.721583e-04 -8.084112e-04 8.735407e-04 5.949578e-04 4.589616e-05 -3.463711e-04 -4.209386e-04
## PC113 PC114 PC115 PC118 PC119 PC120 PC121 PC122
## 1.352546e-05 -5.608260e-04 -1.514517e-03 1.553867e-04 -7.250585e-04 1.778366e-04 -2.614094e-04 4.757536e-04
## PC123 PC124 PC125 PC127 PC128 PC130 PC131 PC132
## -5.603038e-04 2.979124e-04 3.399717e-04 5.095509e-04 -8.283895e-04 4.218912e-05 -1.050207e-03 4.782348e-05
## PC134 PC135 PC136 PC137 PC138 PC139 PC140 PC143
## 5.470400e-04 1.914542e-04 3.963328e-04 -7.273543e-05 1.690818e-04 -7.524366e-04 -2.408588e-04 2.013255e-04
## PC144 PC145 PC146 PC147 PC148 PC150 PC151 PC152
## 6.076572e-04 1.869404e-04 5.662762e-04 -2.930924e-05 -3.488870e-04 2.723191e-04 4.011508e-04 -3.491758e-04
## PC153 PC154 PC155 PC156 PC159 PC160 PC162 PC163
## 7.098434e-04 -8.940905e-04 8.330511e-04 3.751425e-04 1.406579e-03 -5.149710e-06 -1.260241e-03 4.999147e-04
## PC164
## 1.759616e-04Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.020 2.089 2.100 2.097 2.109 2.131
## [1] "lars Test MSE: 0.000979913265796265"
## [1] "lars Test RMSE: 0.0313035663430904"
## [1] "lars Test MSE (Org Scale): 88.3971956781316"
## [1] "lars Test RMSE (Org Scale): 9.40197828534674"
Session Info
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.20 htmltools_0.3.6 reshape2_1.4.3 lars_1.2
## [5] doParallel_1.0.14 iterators_1.0.10 caret_6.0-81 leaps_3.0
## [9] ggforce_0.1.3 rlist_0.4.6.1 car_3.0-2 carData_3.0-2
## [13] bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0 caTools_1.17.1.1
## [17] mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1 ggstance_0.3.1
## [21] lattice_0.20-35 DT_0.5 ggiraphExtra_0.2.9 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-14
## [29] MASS_7.3-50 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.3.0 stringr_1.3.1 dplyr_0.8.0.1 purrr_0.2.5
## [37] readr_1.3.1 tidyr_0.8.2 tibble_2.1.1 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-4 sp_1.3-1
## [45] pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.2.0 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.1 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.2 gower_0.1.2 colorspace_1.3-2 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.0.0 crayon_1.3.4 jsonlite_1.5 survival_2.42-3 glue_1.3.0 registry_0.5
## [25] gtable_0.2.0 ppcor_1.1 ipred_0.9-8 sjmisc_2.7.9 abind_1.4-5 rngtools_1.3.1
## [31] bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 units_0.6-2 foreign_0.8-70 stats4_3.5.1
## [37] lava_1.6.4 prodlim_2018.04.18 htmlwidgets_1.3 httr_1.4.0 RColorBrewer_1.1-2 pkgconfig_2.0.2
## [43] farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5 rlang_0.3.1 later_0.7.5
## [49] munsell_0.5.0 cellranger_1.1.0 tools_3.5.1 cli_1.0.1 generics_0.0.2 moments_0.14
## [55] sjlabelled_1.0.17 broom_0.5.1 evaluate_0.12 ggdendro_0.1-20 yaml_2.2.0 ModelMetrics_1.2.2
## [61] zip_2.0.1 nlme_3.1-137 doRNG_1.7.1 mime_0.6 xml2_1.2.0 compiler_3.5.1
## [67] rstudioapi_0.8 curl_3.2 tweenr_1.0.1 stringi_1.2.4 highr_0.7 gdtools_0.1.7
## [73] pillar_1.3.1 data.table_1.11.8 bitops_1.0-6 insight_0.1.2 httpuv_1.4.5 R6_2.3.0
## [79] promises_1.0.1 gridExtra_2.3 rio_0.5.16 codetools_0.2-15 assertthat_0.2.0 pkgmaker_0.27
## [85] withr_2.1.2 nortest_1.0-4 mgcv_1.8-24 hms_0.4.2 quadprog_1.5-5 grid_3.5.1
## [91] rpart_4.1-13 timeDate_3043.102 class_7.3-14 rmarkdown_1.11 shiny_1.2.0 lubridate_1.7.4